The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition by David Eisenbud (PDF)

Description

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.

User’s Reviews

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). About the Author 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). Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a very very unknown but amazing book on algebraic geometry. The Grothendieck school of abstract is great, but only after one understands the classical picture and approaches first. In this book David used commutative algebra to illustrate how many algebraic geometry we can do knowing only something of the free resolution of the projective coordinate ring (over the polynomial ring). The whole book has a lot of information, and evolves around a development to explain Green’s conjecture and Eisenbud-Goto conjecture. I recommend it highly to any student of algebraic geometry.

⭐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.

⭐A truly excellent book! And at a very good price too

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Free Download The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition in PDF format
The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition PDF Free Download
Download The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition 2005 PDF Free
The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition 2005 PDF Free Download
Download The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition PDF
Free Download Ebook The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics, 229) 2005th Edition