The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra

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 syzygies as they are used in algebraic geometry. It includes geometric examples ranging from interpolation to canonical curves. The text has served as the basis for graduate courses at Berkeley, Brandeis, and in Paris. It is also suitable for self-study b a reader who knows a little commutative algebra and algebraic geometry. As aids to the reader, one appendix gives an introduction to local cohomology and another 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 the University of California, Berkeley. His other books include Commutative Algebra with a View Toward Algebraic Geometry (1995), and The Geometry of Schemes, with Joe Harris (1999)