The Geometry of Syzygies

A second course in algebraic geometry

David Eisenbud - Collection Graduate Texts in Mathematics

250 pages, parution le 22/03/2005

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Résumé

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.

Written for: Graduate students, research mathematicians

Sommaire

Preface: Algebra and Geometry
Free Resolutions and Hilbert Functions
First Examples of Free Resolutions
Points in P²
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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David Eisenbud
Collection	Graduate Texts in Mathematics
Parution	22/03/2005
Nb. de pages	250
Format	15,5 x 23,5
Couverture	Broché
Poids	380g
Intérieur	Noir et Blanc
EAN13	9780387222325
ISBN13	978-0-387-22232-5