Home eBooks Download › the practice of algebraic curves

The Practice Of Algebraic Curves

Download The Practice Of Algebraic Curves PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Practice Of Algebraic Curves book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

The Practice Of Algebraic Curves

DOWNLOAD
Author : David Eisenbud
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-07

The Practice Of Algebraic Curves written by David Eisenbud and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Mathematics categories.

This textbook provides readers with a working knowledge of the modern theory of complex projective algebraic curves. Also known as compact Riemann surfaces, such curves shaped the development of algebraic geometry itself, making this theory essential background for anyone working in or using this discipline. Examples underpin the presentation throughout, illustrating techniques that range across classical geometric theory, modern commutative algebra, and moduli theory. The book begins with two chapters covering basic ideas, including maps to projective space, invertible sheaves, and the Riemann?Roch theorem. Subsequent chapters alternate between a detailed study of curves up to genus six and more advanced topics such as Jacobians, Hilbert schemes, moduli spaces of curves, Severi varieties, dualizing sheaves, and linkage of curves in 3-space. Three chapters treat the refinements of the Brill?Noether theorem, including applications and a complete proof of the basic result. Two chapters on free resolutions, rational normal scrolls, and canonical curves build context for Green?s conjecture. The book culminates in a study of Hilbert schemes of curves through examples. A historical appendix by Jeremy Gray captures the early development of the theory of algebraic curves. Exercises, illustrations, and open problems accompany the text throughout. The Practice of Algebraic Curves offers a masterclass in theory that has become essential in areas ranging from algebraic geometry itself to mathematical physics and other applications. Suitable for students and researchers alike, the text bridges the gap from a first course in algebraic geometry to advanced literature and active research.

The Practice Of Algebraic Curves

DOWNLOAD
Author : David Eisenbud
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-09

Complex Algebraic Curves

DOWNLOAD
Author : Frances Clare Kirwan
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-20

Complex Algebraic Curves written by Frances Clare Kirwan 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 1992-02-20 with Mathematics categories.

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.

Using Algebraic Geometry

DOWNLOAD
Author : David A. Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Using Algebraic Geometry written by David A. Cox 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 2013-04-17 with Mathematics categories.

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

Rational Algebraic Curves

DOWNLOAD
Author : J. Rafael Sendra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-10

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 2007-12-10 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.

3264 And All That

DOWNLOAD
Author : David Eisenbud
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-14

3264 And All That written by David Eisenbud 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 2016-04-14 with Mathematics categories.

3264, the mathematical solution to a question concerning geometric figures.

Elementary Geometry Of Algebraic Curves

DOWNLOAD
Author : C. G. Gibson
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-26

Elementary Geometry Of Algebraic Curves written by C. G. Gibson 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 1998-11-26 with Mathematics categories.

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.

Riemann Surfaces And Algebraic Curves

DOWNLOAD
Author : Renzo Cavalieri
language : en
Publisher: Cambridge University Press
Release Date : 2016-09-26

Riemann Surfaces And Algebraic Curves written by Renzo Cavalieri 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 2016-09-26 with Mathematics categories.

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Effective Methods In Algebraic Geometry

DOWNLOAD
Author : Teo Mora
language : en
Publisher: Springer Science & Business Media
Release Date : 1991

Effective Methods In Algebraic Geometry written by Teo Mora 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 1991 with Mathematics categories.

The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").

Undergraduate Algebraic Geometry

DOWNLOAD
Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 1988-12-15

Undergraduate Algebraic Geometry written by Miles Reid 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 1988-12-15 with Mathematics categories.

Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.

The Practice Of Algebraic Curves

Recent Posts