Graduate Texts in Mathematics

The Geometry of Syzygies

A Second Course in Algebraic Geometry and Commutative Algebra

Authors: Eisenbud, David

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About this Textbook

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).

About the authors

The author taught at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley, and became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997. At the same time he joined the faculty of UC Berkeley as Professor of Mathematics. In 2003 he became President of the American Mathematical Society. He currently serves on several editorial boards (Annals of Mathematics, Bulletin du Société Mathématique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics).

Reviews

From the reviews:

"This book is devoted to offer … an approach to the study of this algebraic subject (syzygy = relation among generators of a module) … . a student would learn a lot of algebraic geometry from it. The double bet of the book is to be able to be a complete textbook … and at the same time to become a useful reference text for research work on the subject. I would say that both aspects of the bet have been gained … ." (Alessandro Gimigliano, Zentralblatt MATH, Vol. 1066, 2005)

"This book may be regarded as a complement to the author’s Commutative Algebra … . It begins by explaining syzygies and their connection with the Hilbert function, and turns to describing various aspects of algebraic geometry … . Two appendices provide the background in commutative algebra and local cohomology. Together with exercises, it gives a good survey of topics often not covered." (Mathematika, Vol. 52, 2005)

"This monograph is devoted to the geometric properties of a projective variety corresponding to the properties of its syzygies … . Altogether, this is a most welcome addition to the literature and will help many a reader bridge the gap between the abstractions of algebra and the more tangible field of geometry." (Ch. Baxa, Monatshefte für Mathematik, Vol. 150 (1), 2006)

Aus den Rezensionen: “... Das vorliegende Buch beschäftigt sich mit der qualitativen geometrischen Theorie der Syzygien. ... Es gibt zwei sehr kompakt geschriebene Anhänge: Der erste führt in die lokale Kohomologie ein, der zweite stellt für das Buch nötige Vorkenntnisse der kommutativen Algebra ... zusammen. Dieses Buch ist sehr elegant geschrieben und vermittelt viele interessante Ideen. In der Lehre könnte es gut für weiterführende Vorlesungen über algebraische Geometrie verwendet werden.“ (Franz Pauer, in: Internationale Mathematische Nachrichten, December/2009, Issue 12, S. 45)

“This very interesting book is the first textbook-level account of syzygies as they are used in algebraic geometry. … The reader will find two very good and useful appendices. … The book can be read, without any problem, by a student who has received already a little introduction in commutative algebra and algebraic geometry. I highly recommend this nice and deep textbook for all students and researchers studying algebraic geometry or commutative algebra.” (Dominique Lambert, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)


Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-0-387-26456-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-22215-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • ISBN 978-0-387-22232-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Geometry of Syzygies
Book Subtitle
A Second Course in Algebraic Geometry and Commutative Algebra
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
229
Copyright
2005
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-26456-1
DOI
10.1007/b137572
Hardcover ISBN
978-0-387-22215-8
Softcover ISBN
978-0-387-22232-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIV, 246
Topics