Описание: Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics.
Описание: Here is the first part of a two volume work that contains a contemporary account of positivity in complex algebraic geometry. Topics in this volume include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity.
Описание: This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.
Описание: This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover edition as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".
Описание: This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments.
Описание: This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators.
Автор: JГјttler Bert, Piene Ragni Название: Geometric Modeling and Algebraic Geometry ISBN: 3540721843 ISBN-13(EAN): 9783540721840 Издательство: Springer Рейтинг: Цена: 20789 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The two fields of Geometric Modeling and Algebraic Geometry, thoughclosely related, are traditionally represented by two almost disjointscientific communities. Both fields deal with objects defined byalgebraic equations, but the objects are studied in different ways.This contributed book presents, in 12 chapters written byleading experts, recent results which rely on theinteraction of both fields. Some of these results have been obtainedin the frame of the European GAIA II project (IST 2001-35512) entitled`Intersection algorithms for geometry-based IT applications usingapproximate algebraic methods'.
Автор: Cox Название: Using Algebraic Geometry ISBN: 0387207333 ISBN-13(EAN): 9780387207339 Издательство: Springer Рейтинг: Цена: 6081 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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 GrГ¶bner 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 GrГ¶bner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.
Автор: Debarre Olivier Название: Higher-Dimensional Algebraic Geometry ISBN: 0387952276 ISBN-13(EAN): 9780387952277 Издательство: Springer Рейтинг: Цена: 10394 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Higher-dimensional algebraic geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authorВїs goal is to provide an easily accessible introduction to the subject. The book covers preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards MoriВїs minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers.
Автор: Cox David A., Little John, O`Shea Donal Название: Using Algebraic Geometry ISBN: 0387207066 ISBN-13(EAN): 9780387207063 Издательство: Springer Рейтинг: Цена: 13209 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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 GrГ¶bner 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 GrГ¶bner bases. The book does not assume the reader is familiar with more advanced concepts such as modules. For this new edition the authors added two new sections and a new chapter, updated the references and made numerous minor improvements throughout the text.
Описание: Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves. The text has served as a basis for graduate courses by the author at Berkeley, Brandeis, and in Paris. It is also suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. As an aid to the reader, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics.
