Algebraic Curves

Author : William Fulton
Publisher :
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.05/5 ( download)

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Download or read book Algebraic Curves written by William Fulton and published by . This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideals and polynomials, such as is often covered in a one-semester course in modern algebra; additional commutative algebra is developed in later sections.

Author : Edward Frenkel
Publisher : American Mathematical Soc.
ISBN 13 : 0821836749
Total Pages : 418 pages
Book Rating : 4.43/5 ( download)

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Download or read book Vertex Algebras and Algebraic Curves written by Edward Frenkel and published by American Mathematical Soc.. This book was released on 2004-08-25 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.

Author : Frances Clare Kirwan
Publisher : Cambridge University Press
ISBN 13 : 9780521423533
Total Pages : 278 pages
Book Rating : 4.38/5 ( download)

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Download or read book Complex Algebraic Curves written by Frances Clare Kirwan and published by Cambridge University Press. This book was released on 1992-02-20 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Author : BRIESKORN
Publisher : Birkhäuser
ISBN 13 : 3034850972
Total Pages : 730 pages
Book Rating : 4.71/5 ( download)

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Download or read book Plane Algebraic Curves written by BRIESKORN and published by Birkhäuser. This book was released on 2013-11-11 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Eduardo Casas-Alvero
Publisher : Springer Nature
ISBN 13 : 3030290166
Total Pages : 224 pages
Book Rating : 4.60/5 ( download)

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Download or read book Algebraic Curves, the Brill and Noether Way written by Eduardo Casas-Alvero and published by Springer Nature. This book was released on 2019-11-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Harold Hilton
Publisher :
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.68/5 ( download)

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Download or read book Plane Algebraic Curves written by Harold Hilton and published by . This book was released on 1920 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Rick Miranda
Publisher : American Mathematical Soc.
ISBN 13 : 0821802682
Total Pages : 414 pages
Book Rating : 4.87/5 ( download)

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Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

Author : Robert J. Walker
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.00/5 ( download)

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Download or read book Algebraic Curves written by Robert J. Walker and published by . This book was released on 1955 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Keith Kendig
Publisher : MAA
ISBN 13 : 0883853531
Total Pages : 211 pages
Book Rating : 4.35/5 ( download)

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Download or read book A Guide to Plane Algebraic Curves written by Keith Kendig and published by MAA. This book was released on 2011 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the plane algebraic curves that also serves as a natural entry point to algebraic geometry. This book can be used for an undergraduate course, or as a companion to algebraic geometry at graduate level.

Author : J. Rafael Sendra
Publisher : Springer Science & Business Media
ISBN 13 : 3540737251
Total Pages : 273 pages
Book Rating : 4.54/5 ( download)

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Download or read book Rational Algebraic Curves written by J. Rafael Sendra and published by Springer Science & Business Media. This book was released on 2007-12-10 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.