Using Algebraic Geometry

But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

DOWNLOAD NOW »

Author: David A. Cox

Publisher: Springer Science & Business Media

ISBN: 9781475769111

Category: Mathematics

Page: 503

View: 167

An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

Commutative Algebra

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with ...

DOWNLOAD NOW »

Author: David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 9781461253501

Category: Mathematics

Page: 800

View: 320

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Computing in Algebraic Geometry

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations.

DOWNLOAD NOW »

Author: Wolfram Decker

Publisher: Springer Science & Business Media

ISBN: 9783540289920

Category: Mathematics

Page: 328

View: 625

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Algebraic Geometry

This book introduces the reader to modern algebraic geometry.

DOWNLOAD NOW »

Author: Ulrich Görtz

Publisher: Springer Science & Business Media

ISBN: 9783834897220

Category: Mathematics

Page: 615

View: 799

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Algebraic Geometry

This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.

DOWNLOAD NOW »

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 9781475738490

Category: Mathematics

Page: 496

View: 731

An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Computations in Algebraic Geometry with Macaulay 2

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications.

DOWNLOAD NOW »

Author: David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 3540422307

Category: Mathematics

Page: 329

View: 892

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Algebraic Geometry I Schemes

The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes.

DOWNLOAD NOW »

Author: Ulrich Görtz

Publisher: Springer Nature

ISBN: 9783658307332

Category: Mathematics

Page: 626

View: 194

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Computational Methods in Commutative Algebra and Algebraic Geometry

From the reviews of the hardcover edition: "... Many parts of the book can be read by anyone with a basic abstract algebra course.

DOWNLOAD NOW »

Author: Wolmer Vasconcelos

Publisher: Springer Science & Business Media

ISBN: 3540213112

Category: Mathematics

Page: 408

View: 675

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

An Introduction to Algebraic Geometry and Algebraic Groups

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine ...

DOWNLOAD NOW »

Author: Meinolf Geck

Publisher: Clarendon Press

ISBN: 9780191663727

Category: Mathematics

Page: 320

View: 315

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Algebraic Geometry

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way.

DOWNLOAD NOW »

Author: Joe Harris

Publisher: Springer Science & Business Media

ISBN: 9781475721898

Category: Mathematics

Page: 330

View: 674

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Combinatorial Convexity and Algebraic Geometry

The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties.

DOWNLOAD NOW »

Author: Günter Ewald

Publisher: Springer Science & Business Media

ISBN: 9781461240440

Category: Mathematics

Page: 374

View: 256

The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.

Algorithms in Algebraic Geometry

This volume of articles captures some of the spirit of the IMA workshop. In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric compuation.

DOWNLOAD NOW »

Author: Alicia Dickenstein

Publisher: Springer Science & Business Media

ISBN: 0387751556

Category: Mathematics

Page: 162

View: 722

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.

Algebraic Geometry for Coding Theory and Cryptography

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation ...

DOWNLOAD NOW »

Author: Everett W. Howe

Publisher: Springer

ISBN: 9783319639314

Category: Mathematics

Page: 150

View: 257

Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.

Geometric Modeling and Algebraic Geometry

In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.

DOWNLOAD NOW »

Author: Bert Jüttler

Publisher: Springer Science & Business Media

ISBN: 3540721851

Category: Mathematics

Page: 231

View: 198

Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. In 12 chapters written by leading experts, this book presents recent results which rely on the interaction of both fields. Some of these results have been obtained from a major European project in geometric modeling.

Introduction to Algebraic Geometry

Originally published in 1950, this textbook studies projective geometry and provides a solid introduction to similar studies in space of more than two dimensions.

DOWNLOAD NOW »

Author: W. Gordon Welchman

Publisher: Cambridge University Press

ISBN: 9781316601808

Category: Mathematics

Page: 349

View: 316

Originally published in 1950, this textbook studies projective geometry and provides a solid introduction to similar studies in space of more than two dimensions.

A First Course in Computational Algebraic Geometry

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

DOWNLOAD NOW »

Author: Wolfram Decker

Publisher: Cambridge University Press

ISBN: 9781107612532

Category: Computers

Page: 118

View: 987

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Algorithms in Real Algebraic Geometry

Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

DOWNLOAD NOW »

Author: Saugata Basu

Publisher: Springer Science & Business Media

ISBN: 9783662053553

Category: Mathematics

Page: 602

View: 756

In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

Hilbert s Tenth Problem

This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry.

DOWNLOAD NOW »

Author: Ernst Dieterichs

Publisher: American Mathematical Soc.

ISBN: 9780821826225

Category: Mathematics

Page: 367

View: 952

This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest. The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bucchi's problem, and results on the complexity of diophantine geometry, highlighting the relation to the theory of computation.The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory.

Algebraic Geometry and Commutative Algebra

The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.

DOWNLOAD NOW »

Author: Siegfried Bosch

Publisher: Springer Science & Business Media

ISBN: 9781447148296

Category: Mathematics

Page: 504

View: 351

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.

Algebraic Geometry

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 ...

DOWNLOAD NOW »

Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 9780486154725

Category: Mathematics

Page: 256

View: 916

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.