Using Algebraic Geometry

Autor: David A Cox
Publisher: Springer Science & Business Media
ISBN: 1475769113
File Size: 54,39 MB
Format: PDF, Mobi
Read: 3341
Download or Read Book
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.

Algebraic Geometry

Autor: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 1475738498
File Size: 18,14 MB
Format: PDF, Mobi
Read: 5873
Download or Read Book
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.

Algebraic Geometry

Autor: Elena Rubei
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110316234
File Size: 69,42 MB
Format: PDF, ePub, Mobi
Read: 2172
Download or Read Book
Algebraic geometry has a complicated, difficult language. This book contains a definition, several references and the statements of the main theorems (without proofs) for every of the most common words in this subject. Some terms of related subjects are included. It helps beginners that know some, but not all, basic facts of algebraic geometry to follow seminars and to read papers. The dictionary form makes it easy and quick to consult.

Algebraic Geometry

Autor: Joe Harris
Publisher: Springer Science & Business Media
ISBN: 1475721897
File Size: 58,95 MB
Format: PDF, ePub, Mobi
Read: 1770
Download or Read Book
"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

Algebraic Geometry Sheaves And Cohomology

Autor: 健爾·上野
Publisher: American Mathematical Soc.
ISBN: 9780821813577
File Size: 28,36 MB
Format: PDF, ePub, Mobi
Read: 2977
Download or Read Book
Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes is presented in the first part of this book (Algebraic Geometry 1: From Algebraic Varieties to Schemes, AMS, 1999, Translations of Mathematical Monographs, Volume 185). In the present book, the author turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local algebraic functions on an algebraic manifold or the local sections of a vector bundle. Sheaf cohomology is a primary tool in understanding sheaves and using them to study properties of the corresponding manifolds. The text covers the important topics of the theory of sheaves on algebraic varieties, including types of sheaves and the fundamental operations on them, such as coherent and quasicoherent sheaves, direct and inverse images, behavior of sheaves under proper and projective morphisms, and Cech cohomology. The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry.

Analytic Combinatorics In Several Variables

Autor: Robin Pemantle
Publisher: Cambridge University Press
ISBN: 1107031575
File Size: 27,36 MB
Format: PDF
Read: 140
Download or Read Book
This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.

Interactions Of Classical And Numerical Algebraic Geometry

Autor: Daniel James Bates
Publisher: American Mathematical Soc.
ISBN: 0821847465
File Size: 21,86 MB
Format: PDF, Docs
Read: 8076
Download or Read Book
This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.

An Invitation To Algebraic Geometry

Autor: Karen E. Smith
Publisher: Springer Science & Business Media
ISBN: 9780387989808
File Size: 53,95 MB
Format: PDF, ePub
Read: 6246
Download or Read Book
The underlying principles of algebraic geometry, 20th-century developments, and the challenges facing practitioners today are discussed in this book, intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry.

Algebraic Geometry From Algebraic Varieties To Schemes

Autor: 健爾·上野
Publisher: American Mathematical Soc.
ISBN: 9780821808627
File Size: 24,25 MB
Format: PDF
Read: 6316
Download or Read Book
This is the first of three volumes on algebraic geometry. The second volume, Algebraic Geometry 2: Sheaves and Cohomology, is available from the AMS as Volume 197 in the Translations of Mathematical Monographs series. Early in the 20th century, algebraic geometry underwent a significant overhaul, as mathematicians, notably Zariski, introduced a much stronger emphasis on algebra and rigor into the subject. This was followed by another fundamental change in the 1960s with Grothendieck's introduction of schemes. Today, most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an inviting introduction to the theory, which should overcome any such impediment to learning this rich subject. The book begins with a description of the standard theory of algebraic varieties. Then, sheaves are introduced and studied, using as few prerequisites as possible. Once sheaf theory has been well understood, the next step is to see that an affine scheme can be defined in terms of a sheaf over the prime spectrum of a ring. By studying algebraic varieties over a field, Ueno demonstrates how the notion of schemes is necessary in algebraic geometry. This first volume gives a definition of schemes and describes some of their elementary properties. It is then possible, with only a little additional work, to discover their usefulness. Further properties of schemes will be discussed in the second volume. Ueno's book is a self-contained introduction to this important circle of ideas, assuming only a knowledge of basic notions from abstract algebra (such as prime ideals). It is suitable as a text for an introductory course on algebraic geometry.

Algebraic Function Fields And Codes

Autor: Henning Stichtenoth
Publisher: Springer Science & Business Media
ISBN: 3540768785
File Size: 20,47 MB
Format: PDF, Docs
Read: 2471
Download or Read Book
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.