Introduction To Plane Algebraic Curves

Author by : Ernst Kunz
Languange : en
Publisher by : Springer Science & Business Media
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Description : * Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook


Plane Algebraic Curves

Author by : Egbert Brieskorn
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 22
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Description : In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the authorsʼ concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities. --- In the first chapter one finds many special curves with very attractive geometric presentations ‒ the wealth of illustrations is a distinctive characteristic of this book ‒ and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book ‒ and how else could it be with the first author ‒ is the chapter on the resolution of singularities (always over the complex numbers). (...) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)


Plane Algebraic Curves

Author by : Egbert Brieskorn
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 61
Total Download : 325
File Size : 43,8 Mb
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Description : In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, “Plane Algebraic Curves” reflects the authorsʼ concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities. --- In the first chapter one finds many special curves with very attractive geometric presentations ‒ the wealth of illustrations is a distinctive characteristic of this book ‒ and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout’s theorem and a detailed discussion of cubics. The heart of this book ‒ and how else could it be with the first author ‒ is the chapter on the resolution of singularities (always over the complex numbers). (...) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)


A Guide To Plane Algebraic Curves

Author by : Keith Kendig
Languange : en
Publisher by : MAA
Format Available : PDF, ePub, Mobi
Total Read : 81
Total Download : 191
File Size : 45,8 Mb
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Description : This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the subject, while at the same time keeping the exposition simple and understandable, by introducing abstract concepts with concrete examples and pictures. It can be used as the text for an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at graduate level. This book is accessible to those with a limited mathematical background. This is because for those outside mathematics there is a growing need for an entre to algebraic geometry, a need created by the ever-expanding role algebraic geometry is playing in areas ranging from biology to chemistry and robotics to cryptology.


Plane Algebraic Curves

Author by : Gerd Fischer
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 84
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Description : This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.


Introduction To Algebraic Curves

Author by : Phillip A. Griffiths
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 633
File Size : 52,7 Mb
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Description : This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises this book would make an excellent introductory text.


Studyguide For Introduction To Plane Algebraic Curves By Ernst Kunz Isbn 9780817643812

Author by : Cram101 Textbook Reviews
Languange : en
Publisher by : Cram101
Format Available : PDF, ePub, Mobi
Total Read : 40
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Description : Never HIGHLIGHT a Book Again! Virtually all of the testable terms, concepts, persons, places, and events from the textbook are included. Cram101 Just the FACTS101 studyguides give all of the outlines, highlights, notes, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanys: 9780817643812 .


An Introduction To Algebraic Geometry

Author by : Kenji Ueno
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 51
Total Download : 597
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Description : This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.


Plane Algebraic Curves

Author by : C. Orzech
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 69
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A Treatise On Algebraic Plane Curves

Author by : Julian Lowell Coolidge
Languange : en
Publisher by : Courier Corporation
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 654
File Size : 55,9 Mb
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Description : A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.


Plane Algebraic Curves

Author by : C. Orzech
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 33
Total Download : 147
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Description : This book introduces the contemporary notions of algebraic varieties, morphisms of varieties, and adeles to the classical subject of plane curves over algebraically closed fields. It is useful for advanced undergraduate and beginning graduate students in mathematics.


Elementary Geometry Of Algebraic Curves

Author by : C. G. Gibson
Languange : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 21
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Description : Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.


A Guide To Plane Algebraic Curves

Author by : Keith Kendig
Languange : en
Publisher by : Mathematical Association of America
Format Available : PDF, ePub, Mobi
Total Read : 43
Total Download : 696
File Size : 51,8 Mb
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Description : This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the subject, while at the same time keeping the exposition simple and understandable, by introducing abstract concepts with concrete examples and pictures. It can be used as the text for an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at graduate level. This book is accessible to those with a limited mathematical background. This is because for those outside mathematics there is a growing need for an entrée to algebraic geometry, a need created by the ever-expanding role algebraic geometry is playing in areas ranging from biology to chemistry and robotics to cryptology.


Introduction To Algebraic Geometry

Author by : John Greenlees Semple
Languange : en
Publisher by : Oxford University Press, USA
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 795
File Size : 47,8 Mb
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Description : This classic work, now available in paperback, outlines the geometric aspects of algebraic equations, one of the oldest and most central subjects in mathematics. Recent decades have seen explosive growth in the more abstract side of algeraic geometry, with great emphasis on new basic techniques. This timely reissue complements these recent innovations, providing a much-needed background in such areas as plane curves, quadratic transformations, the geometry of line systems, and the projective characters of curves and surfaces. Providing a wealth of definitive material, this work will appeal to those interested in algebraic geometry and in more modern abstract studies.


Plane Algebraic Curves

Author by : BRIESKORN
Languange : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 87
Total Download : 319
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Description :


Algebraic Curves The Brill And Noether Way

Author by : Eduardo Casas-Alvero
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 74
Total Download : 212
File Size : 49,6 Mb
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Description : The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.


Rational Algebraic Curves

Author by : J. Rafael Sendra
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 992
File Size : 46,8 Mb
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Description : The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.


Conics And Cubics

Author by : Robert Bix
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 282
File Size : 49,5 Mb
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Description : Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.


Algebraic Curves

Author by : William Fulton
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 47
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Description :


Algebraic Geometry I

Author by : V.I. Danilov
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 90
Total Download : 645
File Size : 52,5 Mb
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Description : "... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum


Algebraic Curves

Author by : Maxim E. Kazaryan
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 90
Total Download : 335
File Size : 55,6 Mb
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Description : This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework


A Guide To Plane Algebraic Curves

Author by : Keith Kendig
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 96
Total Download : 915
File Size : 55,7 Mb
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Description : An accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry.


Algebraic Curves Over A Finite Field

Author by : J. W. P. Hirschfeld
Languange : en
Publisher by : Princeton University Press
Format Available : PDF, ePub, Mobi
Total Read : 69
Total Download : 823
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Description : This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.


An Introduction To The Theory Of Special Divisors On Algebraic Curves

Author by : Phillip Griffiths
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 43
Total Download : 257
File Size : 43,5 Mb
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Description : In May, 1979, an NSF Regional Conference was held at the University of Georgia in Athens. The topic of the conference was ``Special divisors on algebraic curves,''. This monograph gives an exposition of the elementary aspects of the theory of special divisors together with an explanation of some more advanced results that are not too technical. As such, it is intended to be an introduction to recent sources. As with most subjects, one may approach the theory of special divisors from several points of view. The one adopted here pertains to Clifford's theorem, and may be informally stated as follows: The failure of a maximally strong version of Clifford's theorem to hold imposes nontrivial conditions on the moduli of an algebraic curve. This monograph contains two sections, respectively studying special divisors using the Riemann-Roch theorem and the Jacobian variety. In the first section the author begins pretty much at ground zero, so that a reader who has only passing familiarity with Riemann surfaces or algebraic curves may be able to follow the discussion. The respective subtopics in this first section are (a) the Riemann-Roch theorem, (b) Clifford's theorem and the $\mu_0$-mapping, and (c) canonical curves and the Brill-Noether matrix. In the second section he assumes a little more, although again an attempt has been made to explain, if not prove, anything. The respective subtopics are (a) Abel's theorem, (b) the reappearance of the Brill-Noether matrix with applications to the singularities of $W_d$ and the Kleiman-Laksov existence proof, (c) special linear systems in low genus.


Singularities Algebraic Geometry Commutative Algebra And Related Topics

Author by : Gert-Martin Greuel
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 58
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Description : This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.


Real Algebraic Geometry

Author by : Michel Coste
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 39
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Description : Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.


Lectures On Curves Surfaces And Projective Varieties

Author by : Mauro Beltrametti
Languange : en
Publisher by : European Mathematical Society
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 212
File Size : 53,5 Mb
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Description : This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.


Rational Algebraic Curves

Author by : J. Rafael Sendra
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 81
Total Download : 826
File Size : 54,5 Mb
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Description : The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.