First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.
The Geometry of Syzygies
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Editorial Reviews
Review
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)
From the Back Cover
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).
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
Great book,
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This review is from: The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics) (Paperback)
Great book. It is really worthy the money, especially if you want to better understand geometry from an algebraic perspectives. For pure geometers it might be a little bit too algebraic.
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Inside This Book
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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. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quadratic strand, twisted global sections, general line bundle, exterior minors, graded betti numbers, minimal free resolution, complete linear series, elliptic normal curve, nonhyperelliptic curve, rational normal curve, generalized rows, nondegenerate curve, noncolinear points, imposes independent conditions, rational normal scrolls, linear syzygies, impose independent conditions, graded free resolution, monomial ideal, determinantal ideals, projective dimension, canonical series, finitely generated graded module, local cohomology, linear strand Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cohen Macaulay, Linear Syzygy Theorem, Principal Ideal Theorem, Eagon Northcott, Characterizations of Regularity, Using Proposition, Green's Theorem, Hilbert Syzygy Theorem, Serre's Criterion New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A minimal free resolution is an invariant associated to a graded module over a ring graded by the natural numbers N or by Nn. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
quadratic strand, twisted global sections, general line bundle, exterior minors, graded betti numbers, minimal free resolution, complete linear series, elliptic normal curve, nonhyperelliptic curve, rational normal curve, generalized rows, nondegenerate curve, noncolinear points, imposes independent conditions, rational normal scrolls, linear syzygies, impose independent conditions, graded free resolution, monomial ideal, determinantal ideals, projective dimension, canonical series, finitely generated graded module, local cohomology, linear strand Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cohen Macaulay, Linear Syzygy Theorem, Principal Ideal Theorem, Eagon Northcott, Characterizations of Regularity, Using Proposition, Green's Theorem, Hilbert Syzygy Theorem, Serre's Criterion New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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- Algebraic Number Theory (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), Back Matter (2), and Back Matter (3)
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter (1), and Back Matter (2)
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Differential Equations: Dynamical Systems, and Control Science: Lecture Notes in Pure and Applied Mathematics Series/152 by K.D. Elworthy in Back Matter (1), and Back Matter (2)
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
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