Symplectic 4 Manifolds And Algebraic Surfaces

Author by : Fabrizio Catanese
Languange : en
Publisher by : Springer
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Description : Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.


Symplectic 4 Manifolds And Algebraic Surfaces

Author by : Fabrizio Catanese
Languange : en
Publisher by : Springer
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Description : Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.


Geometry Of Low Dimensional Manifolds Volume 1 Gauge Theory And Algebraic Surfaces

Author by : LMS Durham Symposium (1989)
Languange : en
Publisher by : Cambridge University Press
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Description : Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.


Algebraic Surfaces And Holomorphic Vector Bundles

Author by : Robert Friedman
Languange : en
Publisher by : Springer Science & Business Media
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Description : A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.


History Of Topology

Author by : I.M. James
Languange : en
Publisher by : Elsevier
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Description : Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards. As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.


Donaldson Type Invariants For Algebraic Surfaces

Author by : Takuro Mochizuki
Languange : en
Publisher by : Springer
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Description : In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ̈ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.


Handbook Of Teichm Ller Theory

Author by : Athanase Papadopoulos
Languange : en
Publisher by : European Mathematical Society
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Description : This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.


Complex And Differential Geometry

Author by : Wolfgang Ebeling
Languange : en
Publisher by : Springer Science & Business Media
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Description : This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.


Classification Of Algebraic Varieties

Author by : Carel Faber
Languange : en
Publisher by : European Mathematical Society
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Description : Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.


Galois Covers Grothendieck Teichm Ller Theory And Dessins D Enfants

Author by : Frank Neumann
Languange : en
Publisher by : Springer Nature
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Description : This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.


Geometric Topology

Author by : William Hilal Kazez
Languange : en
Publisher by : American Mathematical Soc.
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Description : This is Part 2 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.


Recent Advances In Algebraic Geometry

Author by : Christopher D. Hacon
Languange : en
Publisher by : Cambridge University Press
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Description : A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.


J Holomorphic Curves And Symplectic Topology

Author by : Dusa McDuff
Languange : en
Publisher by : American Mathematical Soc.
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Description : This second edition continues to serve as the definitive source of information about some areas of differential topology ($J$-holomorphic curves) and applications to quantum cohomology. The main goal of the book is to establish the fundamental theorems of the subject in full and rigorous detail. It may also serve as an introduction to current work in symplectic topology. The second edition clarifies various arguments, includes some additional results, and updates the references to recent developments.


Lectures On K3 Surfaces

Author by : Daniel Huybrechts
Languange : en
Publisher by : Cambridge University Press
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Description : Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.


Topology Geometry And Dynamics V A Rokhlin Memorial

Author by : Anatoly M. Vershik
Languange : en
Publisher by : American Mathematical Soc.
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Description : Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.


Algebraic Geometry Santa Cruz 1995

Author by : János Kollár
Languange : en
Publisher by : American Mathematical Soc.
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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.


First European Congress Of Mathematics

Author by : Anthony Joseph
Languange : en
Publisher by : Birkhäuser
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Description : Table of contents: Plenary Lectures V.I. Arnold: The Vassiliev Theory of Discriminants and Knots L. Babai: Transparent Proofs and Limits to Approximation C. De Concini: Poisson Algebraic Groups and Representations of Quantum Groups at Roots of 1 S.K. Donaldson: Gauge Theory and Four-Manifold Topology W. Mller: Spectral Theory and Geometry D. Mumford: Pattern Theory: A Unifying Perspective A.-S. Sznitman: Brownian Motion and Obstacles M. Vergne: Geometric Quantization and Equivariant Cohomology Parallel Lectures Z. Adamowicz: The Power of Exponentiation in Arithmetic A. Bjrner: Subspace Arrangements B. Bojanov: Optimal Recovery of Functions and Integrals J.-M. Bony: Existence globale et diffusion pour les modles discrets R.E. Borcherds: Sporadic Groups and String Theory J. Bourgain: A Harmonic Analysis Approach to Problems in Nonlinear Partial Differatial Equations F. Catanese: (Some) Old and New Results on Algebraic Surfaces Ch. Deninger: Evidence for a Cohomological Approach to Analytic Number Theory S. Dostoglou and D.A. Salamon: Cauchy-Riemann Operators, Self-Duality, and the Spectral Flow.


Real And Complex Singularities

Author by : Ana Claudia Nabarro
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)


Cyclic Coverings Calabi Yau Manifolds And Complex Multiplication

Author by : Christian Rohde
Languange : en
Publisher by : Springer
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Description : Calabi-Yau manifolds have been an object of extensive research during the last two decades. One of the reasons is the importance of Calabi-Yau 3-manifolds in modern physics - notably string theory. An interesting class of Calabi-Yau manifolds is given by those with complex multiplication (CM). Calabi-Yau manifolds with CM are also of interest in theoretical physics, e. g. in connection with mirror symmetry and black hole attractors. It is the main aim of this book to construct families of Calabi-Yau 3-manifolds with dense sets of ?bers with complex multiplication. Most - amples in this book are constructed using families of curves with dense sets of ?bers with CM. The contents of this book can roughly be divided into two parts. The ?rst six chapters deal with families of curves with dense sets of CM ?bers and introduce the necessary theoretical background. This includes among other things several aspects of Hodge theory and Shimura varieties. Using the ?rst part, families of Calabi-Yau 3-manifolds with dense sets of ?bers withCM are constructed in the remaining ?ve chapters. In the appendix one ?nds examples of Calabi-Yau 3-manifolds with complex mul- plication which are not necessarily ?bers of a family with a dense set ofCM ?bers. The author hopes to have succeeded in writing a readable book that can also be used by non-specialists.


Integrability Quantization And Geometry Ii Quantum Theories And Algebraic Geometry

Author by : Sergey Novikov
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.


Featured Reviews In Mathematical Reviews 1997 1999

Author by : Donald G. Babbitt
Languange : en
Publisher by : American Mathematical Soc.
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Description : This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.


Endoscopy For Gsp 4 And The Cohomology Of Siegel Modular Threefolds

Author by : Rainer Weissauer
Languange : en
Publisher by : Springer Science & Business Media
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Description : The geometry of modular curves and the structure of their cohomology groups have been a rich source for various number-theoretical applications over the last decades. Similar applications may be expected from the arithmetic of higher dimensional modular varieties. For Siegel modular threefolds some basic results on their cohomology groups are derived in this book from considering topological trace formulas.


Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures

Author by : Bhatia Rajendra
Languange : en
Publisher by : World Scientific
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Description : ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.


Symmetries Of Compact Riemann Surfaces

Author by : Emilio Bujalance
Languange : en
Publisher by : Springer Science & Business Media
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Description : This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.


Problems On Mapping Class Groups And Related Topics

Author by : Benson Farb
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book contains 23 papers of open problems and directions about mapping class groups and related topics. The papers focus on aspects deeply connected with geometric topology, combinatorial group theory and surrounding areas.


Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes

Author by : Sirakov Boyan
Languange : en
Publisher by : World Scientific
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Description : The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.


Low Dimensional Topology

Author by : Tomasz Mrowka
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
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Description :


Geometry And Analysis On Complex Manifolds

Author by : Toshiki Mabuchi
Languange : en
Publisher by : World Scientific
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Total Read : 60
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Description : This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.


Geometry And Analysis On Complex Manifolds

Author by : T Mabuchi
Languange : en
Publisher by : World Scientific
Format Available : PDF, ePub, Mobi
Total Read : 97
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Description : This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992. The principal theme of this volume is “Geometry and Analysis on Complex Manifolds”. It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kähler metrics and Einstein–Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kähler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions. Contents:Complex Finsler Metrics (M Abate & G Patrizio)Stable Sheaves and Einstein–Hermitian Metrics (S Bando & Y-T Siu)Generalizations of Albanese Mappings for Non-Kähler Manifolds (I Enoki)Examples of Compact Holomorphic Symplectic Manifolds which Admit No Kähler Structure (D Guan)A Torelli-Type Theorem for Stable Curves (Y Imayoshi & T Mabuchi)Linear Algebra of Analytic Torsion (H-J Kim)KP Equations and Vector Bundles on Curves (Y-C Li)Some Topics in Nevanlinna Theory, Hyperbolic Manifolds and Diophantine Geometry (J Noguchi)On the Extension of L2 Holomorphic Functions IV: A New Density Concept (T Ohsawa)Symplectic Topology and Complex Surfaces (Y-B Ruan)Automorphisms of Tube Domains (S Shimizu)Tensor Products of Semistables are Semistable (B Totaro) Readership: Mathematicians. keywords:Geometry;Analysis;Complex Manifolds;Festschrift