The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry (Graduate Texts in Mathematics)

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). 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) "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.

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.

"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 by 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."--Jacket Free Resolutions and Hilbert Functions....Pages 1-13 First Examples of Free Resolutions....Pages 15-30 Points in P 2 ....Pages 31-54 Castelnuovo-Mumford Regularity....Pages 55-71 The Regularity of Projective Curves....Pages 73-87 Linear Series and 1-Generic Matrices....Pages 89-117 Linear Complexes and the Linear Syzygy Theorem....Pages 119-144 Curves of High Degree....Pages 145-175 Clifford Index and Canonical Embedding....Pages 177-186 A minimal free resolution is an invariant associated to a graded module over a ring graded by the natural numbers N or by Nn.