Representations Of Fundamental Groups Of Algebraic Varieties

Author by : Kang Zuo
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 68
Total Download : 755
File Size : 48,7 Mb
GET BOOK

Description : Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.


Topology Of Algebraic Varieties And Singularities

Author by : Anatoly Libgober
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 35
Total Download : 442
File Size : 52,9 Mb
GET BOOK

Description : This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.


Algebraic Geometry Santa Cruz 1995

Author by : János Kollár
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 518
File Size : 55,8 Mb
GET BOOK

Description : This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz, in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. This book is intended for graduate students and research mathematicains interested in algebraic geometry and related areas.


Galois Groups And Fundamental Groups

Author by : Tamás Szamuely
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 11
Total Download : 316
File Size : 53,9 Mb
GET BOOK

Description : Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.


From Hodge Theory To Integrability And Tqft

Author by : Ron Donagi
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 68
Total Download : 827
File Size : 40,7 Mb
GET BOOK

Description : Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*-geometry (tt* stands for topological-antitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*-geometry has become a fast moving and exciting research area.This book, loosely based on the 2007 Augsburg, Germany workshop ""From tQFT to tt* and Integrability"", is the perfect introduction to the range of mathematical topics relevant to tt*-geometry. It begins with several surveys of the main features of tt*-geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and non-commutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics. With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it.


Fundamental Groups Of Compact K Hler Manifolds

Author by : Jaume Amoros
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 48
Total Download : 402
File Size : 44,6 Mb
GET BOOK

Description : This book is an exposition of what is currently known about the fundamental groups of compact Kahler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterise those infinite groups which can arise as fundamental groups of compact Kahler manifolds. Most of these results are negative ones, saying which groups do not arise. They are proved using Hodge theory and its combinations with rational homotopy theory, with $L^2$-cohomology, with the theory of harmonic maps, and with gauge theory.There are a number of positive results as well, exhibiting interesting groups as fundamental groups of Kahler manifolds, in fact, of smooth complex projective varieties. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.


Geometry And Physics

Author by : Jürgen Jost
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 70
Total Download : 989
File Size : 42,7 Mb
GET BOOK

Description : "Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.


Algebraic Geometry Salt Lake City 2015 Part 1

Author by : Tommaso de Fernex
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 105
File Size : 41,5 Mb
GET BOOK

Description : This is Part 1 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.


Transseries And Real Differential Algebra

Author by : Joris van der Hoeven
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 18
Total Download : 490
File Size : 54,9 Mb
GET BOOK

Description : Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists.


Geometry Of Group Representations

Author by : William Mark Goldman
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 77
Total Download : 138
File Size : 45,6 Mb
GET BOOK

Description : The representations of a finitely generated group in a topological group $G$ form a topological space which is an analytic variety if $G$ is a Lie group, or an algebraic variety if $G$ is an algebraic group. The study of this area draws from and contributes to a wide range of mathematical subjects: algebra, analysis, topology, differential geometry, representation theory, and even mathematical physics. In some cases, the space of representations is the object of the study, in others it is a tool in a program of investigation, and, in many cases, it is both. Most of the papers in this volume are based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987.The conference was designed to bring together researchers from the diverse areas of mathematics involving spaces of group representations. In keeping with the spirit of the conference, the papers are directed at nonspecialists, but contain technical developments to bring the subject to the current research frontier. Some of the papers include entirely new results. Readers will gain an understanding of the present state of research in the geometry of group representations and their applications.


Geometry Of The Plane Cremona Maps

Author by : Maria Alberich-Carramiñana
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 95
Total Download : 942
File Size : 50,9 Mb
GET BOOK

Description : This book provides a self-contained exposition of the theory of plane Cremona maps, reviewing the classical theory. The book updates, correctly proves and generalises a number of classical results by allowing any configuration of singularities for the base points of the plane Cremona maps. It also presents some material which has only appeared in research papers and includes new, previously unpublished results. This book will be useful as a reference text for any researcher who is interested in the topic of plane birational maps.


Osserman Manifolds In Semi Riemannian Geometry

Author by : Eduardo Garcia-Rio
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 92
Total Download : 643
File Size : 46,9 Mb
GET BOOK

Description : The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.


Real Non Abelian Mixed Hodge Structures For Quasi Projective Varieties Formality And Splitting

Author by : J. P. Pridham
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 43
Total Download : 492
File Size : 40,7 Mb
GET BOOK

Description : The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x−i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.


Representation Theories And Algebraic Geometry

Author by : A. Broer
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 79
Total Download : 594
File Size : 49,5 Mb
GET BOOK

Description : The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions. This interplay has been extensively exploited during recent years, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.


Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces

Author by : William Mark Goldman
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 12
Total Download : 963
File Size : 48,8 Mb
GET BOOK

Description : This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkahler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.


Galois Groups And Fundamental Groups

Author by : Tamás Szamuely
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 560
File Size : 42,5 Mb
GET BOOK

Description : Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.


Algebraic Geometry

Author by : Richard Thomas
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 42
Total Download : 593
File Size : 54,5 Mb
GET BOOK

Description : This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.


Asymptotic Behaviour Of Tame Harmonic Bundles And An Application To Pure Twistor D Modules Part 2

Author by : Takuro Mochizuki
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 598
File Size : 44,5 Mb
GET BOOK

Description : The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.


Asymptotic Behaviour Of Tame Harmonic Bundles And An Application To Pure Twistor D Modules Part 1

Author by : Takuro Mochizuki
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 56
Total Download : 185
File Size : 52,9 Mb
GET BOOK

Description : The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.


Calculus Of Variations And Geometric Evolution Problems

Author by : F. Bethuel
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 91
Total Download : 840
File Size : 40,9 Mb
GET BOOK

Description : The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.


Ecole D Ete De Probabilites De Saint Flour

Author by : J. Bertoin
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 60
Total Download : 431
File Size : 42,7 Mb
GET BOOK

Description : Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.


Advances In Geometry

Author by : Jean-Luc Brylinski
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 67
Total Download : 435
File Size : 50,9 Mb
GET BOOK

Description : This book is an outgrowth of the activities of the Center for Geometry and Mathematical Physics (CGMP) at Penn State from 1996 to 1998. The Center was created in the Mathematics Department at Penn State in the fall of 1996 for the purpose of promoting and supporting the activities of researchers and students in and around geometry and physics at the university. The CGMP brings many visitors to Penn State and has ties with other research groups; it organizes weekly seminars as well as annual workshops The book contains 17 contributed articles on current research topics in a variety of fields: symplectic geometry, quantization, quantum groups, algebraic geometry, algebraic groups and invariant theory, and character istic classes. Most of the 20 authors have talked at Penn State about their research. Their articles present new results or discuss interesting perspec tives on recent work. All the articles have been refereed in the regular fashion of excellent scientific journals. Symplectic geometry, quantization and quantum groups is one main theme of the book. Several authors study deformation quantization. As tashkevich generalizes Karabegov's deformation quantization of Kahler manifolds to symplectic manifolds admitting two transverse polarizations, and studies the moment map in the case of semisimple coadjoint orbits. Bieliavsky constructs an explicit star-product on holonomy reducible sym metric coadjoint orbits of a simple Lie group, and he shows how to con struct a star-representation which has interesting holomorphic properties.


Current Topics In Complex Algebraic Geometry

Author by : Clemens Herbert
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 34
Total Download : 968
File Size : 52,9 Mb
GET BOOK

Description : The 1992/93 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. The editors of the volume, Herbert Clemens and János Kollár, chaired the organizing committee. This book gives a good idea of the intellectual content of the special year and of the workshops. Its articles represent very well the change of direction and branching out witnessed by algebraic geometry in the last few years.


Proceedings Of The International Congress Of Mathematicians

Author by : S.D. Chatterji
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 99
Total Download : 933
File Size : 50,7 Mb
GET BOOK

Description : Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)


Different Faces Of Geometry

Author by : Simon Donaldson
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 22
Total Download : 546
File Size : 44,6 Mb
GET BOOK

Description : Different Faces of Geometry presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: -Amoebas and Tropical Geometry; -Convex Geometry and Asymptotic Geometric Analysis; -Differential Topology of 4-Manifolds; -3-Dimensional Contact Geometry; -Floer Homology and Low-Dimensional Topology; -Kdhler Geometry; -Lagrangian and Special Lagrangian Submanifolds; -Refined Seiberg-Witten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USA-Canada-Russia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvath (USA) and Z. Szabs (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany).


Geometry Of Nonpositively Curved Manifolds

Author by : Patrick Eberlein
Languange : en
Publisher by : University of Chicago Press
Format Available : PDF, ePub, Mobi
Total Read : 73
Total Download : 316
File Size : 46,8 Mb
GET BOOK

Description : Starting from the foundations, the author presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two. The book builds to a discussion of the Mostow Rigidity Theorem and its generalizations, and concludes by exploring the relationship in nonpositively curved spaces between geometric and algebraic properties of the fundamental group. This introduction to the geometry of symmetric spaces of non-compact type will serve as an excellent guide for graduate students new to the material, and will also be a useful reference text for mathematicians already familiar with the subject.


Complex Algebraic Varieties

Author by : Klaus Hulek
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 63
Total Download : 494
File Size : 53,7 Mb
GET BOOK

Description : The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibrations revisited.- Th. Peternell, M. Szurek, J.A. Wisniewski: Numerically effective vector bundles with small Chern classes.- C.A.M. Peters: On the rank of non-rigid period maps in the weight one and two case.- A.N. Tyurin: The geometry of the special components of moduli space of vector bundles over algebraic surfaces of general type.


Categorification And Higher Representation Theory

Author by : Anna Beliakova
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 54
Total Download : 516
File Size : 49,7 Mb
GET BOOK

Description : The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory. This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory. The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.


Arithmetic Fundamental Groups And Noncommutative Algebra

Author by : Karen Redrobe Beckman
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 64
Total Download : 573
File Size : 42,7 Mb
GET BOOK

Description : The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G_{\mathbb Q}$ of the algebraic numbers and its close relatives. By analyzing how $G_{\mathbb Q}$ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s.Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.