3264 and All That: A Second Course in Algebraic Geometry 1st Edition by David Eisenbud (PDF)

Description

This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles’ nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré’s development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

User’s Reviews

Editorial Reviews: Review ‘… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.’ Arnaud Beauville, MathSciNet Book Description Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples. About the Author David Eisenbud is Professor of Mathematics at the University of California, Berkeley, and currently serves as Director of the Mathematical Sciences Research Institute. He is also a Director at Math for America, a foundation devoted to improving mathematics teaching.Joe Harris is Professor of Mathematics at Harvard University. Read more

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

⭐All OK

⭐If you already know algebraic geometry, this book gives a relatively coherent account of some really interesting applications of the theory. There are intuitive explanations of concepts and recipes for solving concrete problems. Beyond the TOC you can find in the preview, I would say that this book is a nice intro to moduli spaces, in particular Hilbert schemes.

⭐Eisenbud makes a decisive change of back-ground respect the previous books. He leaves a classical theory about those arguments , prefering a model related to the traditional varieties, but seen by a new view. The interpretation of those spaces depends from the names of Segre, Veronese, Chow, Grothendieck, what that is able to introduce a particular vision of the old geometry.

⭐Excellent condition!

⭐

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