Rational Algebraic Curves

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Rational Algebraic Curves

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Author : J. Rafael Sendra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-19

Rational Algebraic Curves written by J. Rafael Sendra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-19 with Mathematics categories.

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.

Arithmetic Of Algebraic Curves

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Author : Serguei A. Stepanov
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-12-31

Arithmetic Of Algebraic Curves written by Serguei A. Stepanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-31 with Mathematics categories.

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.

Computations With Algebraic Curves

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Author : Shreeram Shankar Abhyankar
language : en
Publisher:
Release Date : 1988

Computations With Algebraic Curves written by Shreeram Shankar Abhyankar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Algebraic Curves

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Author : Robert J. Walker
language : en
Publisher:
Release Date : 1950

Algebraic Curves written by Robert J. Walker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with categories.

Rational Points On Curves Over Finite Fields

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Author : Harald Niederreiter
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-14

Rational Points On Curves Over Finite Fields written by Harald Niederreiter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-14 with Computers categories.

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

Algebraic Curves

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Author : William Fulton
language : en
Publisher:
Release Date : 1969

Algebraic Curves written by William Fulton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Plane Algebraic Curves

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Author : Harold Hilton
language : en
Publisher:
Release Date : 1920

Plane Algebraic Curves written by Harold Hilton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1920 with Curves, Algebraic categories.

Determining Simple Points On Rational Algebraic Curves

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Author : Johannes Kepler Universität Linz. Forschungsinstitut für Symbolisches Rechnen
language : en
Publisher:
Release Date : 1993

Determining Simple Points On Rational Algebraic Curves written by Johannes Kepler Universität Linz. Forschungsinstitut für Symbolisches Rechnen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Local Parameterization Implicitization And Inversion Of Real Algebraic Curves

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Author : Chanderjit Bajaj
language : en
Publisher:
Release Date : 1989

Local Parameterization Implicitization And Inversion Of Real Algebraic Curves written by Chanderjit Bajaj and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

Algebraic Curves Over A Finite Field

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Author : J. W. P. Hirschfeld
language : en
Publisher: Princeton University Press
Release Date : 2013-03-25

Algebraic Curves Over A Finite Field written by J. W. P. Hirschfeld and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Mathematics categories.

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.