Rational Algebraic Curves

Author : J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 51,6 Mb
Release : 2007-12-10
Category : Mathematics
ISBN : 9783540737254

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Rational Algebraic Curves by J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz Pdf

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.

Author : Janos Kollar
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 48,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662032763

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Rational Curves on Algebraic Varieties by Janos Kollar Pdf

The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.

Author : J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 45,5 Mb
Release : 2007-10-19
Category : Mathematics
ISBN : 9783540737247

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Rational Algebraic Curves by J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz Pdf

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.

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 54,5 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 0306110369

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Arithmetic of Algebraic Curves by Serguei A. Stepanov Pdf

Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.

Author : Julian Lowell Coolidge
Publisher : Courier Corporation
Page : 554 pages
File Size : 45,5 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 0486495760

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A Treatise on Algebraic Plane Curves by Julian Lowell Coolidge Pdf

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.

Author : Ernst Kunz
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 53,7 Mb
Release : 2007-06-10
Category : Mathematics
ISBN : 9780817644437

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Introduction to Plane Algebraic Curves by Ernst Kunz Pdf

* 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

Author : Robert John Walker
Publisher : Unknown
Page : 222 pages
File Size : 41,8 Mb
Release : 1950
Category : Mathematics
ISBN : STANFORD:36105004537119

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Algebraic Curves by Robert John Walker Pdf

Author : Gerd Fischer
Publisher : American Mathematical Soc.
Page : 249 pages
File Size : 44,6 Mb
Release : 2001
Category : Curves, Algebraic
ISBN : 9780821821220

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Plane Algebraic Curves by Gerd Fischer Pdf

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.

Author : J. W. P. Hirschfeld,Gabor Korchmaros,Fernando Torres
Publisher : Princeton University Press
Page : 717 pages
File Size : 44,6 Mb
Release : 2013-03-25
Category : Mathematics
ISBN : 9781400847419

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Algebraic Curves over a Finite Field by J. W. P. Hirschfeld,Gabor Korchmaros,Fernando Torres Pdf

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.

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461547853

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Codes on Algebraic Curves by Serguei A. Stepanov Pdf

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.

Author : Frances Clare Kirwan
Publisher : Cambridge University Press
Page : 278 pages
File Size : 55,7 Mb
Release : 1992-02-20
Category : Mathematics
ISBN : 0521423538

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Complex Algebraic Curves by Frances Clare Kirwan Pdf

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 : William Fulton
Publisher : Unknown
Page : 120 pages
File Size : 46,8 Mb
Release : 2008
Category : Mathematics
ISBN : OCLC:1000336205

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Algebraic Curves by William Fulton Pdf

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 : Harald Niederreiter,Chaoping Xing
Publisher : Cambridge University Press
Page : 260 pages
File Size : 49,7 Mb
Release : 2001-06-14
Category : Computers
ISBN : 0521665434

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Rational Points on Curves Over Finite Fields by Harald Niederreiter,Chaoping Xing Pdf

Discussion of theory and applications of algebraic curves over finite fields with many rational points.

Author : Joseph H. Silverman,John Tate
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 50,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742527

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Rational Points on Elliptic Curves by Joseph H. Silverman,John Tate Pdf

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

Author : Eduardo Casas-Alvero
Publisher : Springer Nature
Page : 224 pages
File Size : 50,8 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030290160

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Algebraic Curves, the Brill and Noether Way by Eduardo Casas-Alvero Pdf

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.