Computational algebraic geometry / Hal Schenck.

Format:

Book

Author/Creator:

Schenck, Hal, author.

Series:

London Mathematical Society student texts ; 58.

London Mathematical Society student texts ; 58

Language:

English

Subjects (All):

Geometry, Algebraic--Data processing--Congresses.

Geometry, Algebraic.

Physical Description:

1 online resource (xiv, 193 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2003.

Language Note:

English

Summary:

The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

Contents:

Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Preface; Chapter 1 Basics of Commutative Algebra; Chapter 2 Projective Space and Graded Objects; Chapter 3 Free Resolutions and Regular Sequences; Chapter 4 Gröbner Bases and the Buchberger Algorithm; Chapter 5 Combinatorics, Topology and the Stanley-Reisner Ring; Chapter 6 Functors: Localization, Hom, and Tensor; Chapter 7 Geometry of Points and the Hilbert Function; Chapter 8 Snake Lemma, Derived Functors, Tor and Ext; Chapter 9 Curves, Sheaves, and Cohomology

Chapter 10 Projective Dimension, Cohen-Macaulay Modules, Upper Bound TheoremAppendix A Abstract Algebra Primer; Appendix B Complex Analysis Primer; Bibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 183-187) and index.

ISBN:

1-107-13874-4

0-511-07877-3

9786612389399

1-282-38939-4

0-511-64351-9

0-511-20558-9

0-511-56658-1

0-511-75632-1

0-511-07720-3

OCLC:

171136789