The geometry of syzygies : a second course in commutative algebra and algebraic geometry / David Eisenbud.

Includes bibliographical references (pages [227]-236) and index.

Preface : algebra and geometry 1 Free resolutions and Hilbert functions 1 2 First examples of free resolutions 15 3 Points in P[superscript 2] 31 4 Castelnuovo-Mumford regularity 55 5 The regularity of projective curves 73 6 Linear series and 1-generic matrices 89 7 Linear complexes and the linear syzygy theorem 119 8 Curves of high degree 145 9 Clifford index and canonical embedding 177 App. 1 Introduction to local cohomology 187 App. 2 A jog through commutative algebra 201

"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, the appendices provide summaries of local cohomology and commutative algebra, tying together examples and major results from a wide range of topics."--Publisher's website.