The Geometry of Syzygies
Subtitle: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)
Publisher: Springer
Published: February 1, 2005
Language: eng
Number of pages: 248
ISBN-13: 9780387222325
First sentence: A minimal free resolution is an invariant associated to a graded module over a ring graded by the natural numbers N or by Nn.
Description: "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.