The Geometry of Syzygies

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, an appendix provides a summary of commutative algebra, tying together examples and major results from a wide range of topics.

David Eisenbud is the director of the Mathematical Sciences Research Institute, President of the American Mathematical Society (2003-2004), and Professor of Mathematics at University of California, Berkeley. His other books include Commutative Algebra with a View Toward Algebraic Geometry (1995), and The Geometry of Schemes, with J. Harris (1999).

Auteur

The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).

Texte du rabat

First textbook-level account of basic examples and techniques in this area.

Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.

David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.

Contenu

Preface: Algebra and Geometry Free Resolutions and Hilbert Functions First Examples of Free Resolutions Points in P^2 Castelnuovo-Mumford Regularity The Regularity of Projective Curves Linear Series and 1-Generic Matrices Linear Complexes and the Linear Syzygy Theorem Curves of High Degree Clifford Index and Canonical Embedding Appendix 1: Introduction to Local Cohomology Appendix 2: A Jog Through Commutative Algebra References * Index