The Geometry of Schemes

By: David Eisenbud, Joe Harris

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Hardcover | 1 January 2000

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312 Pages

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The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his co-workers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures in number theory (Deligne's proof of the Weil Conjectures, Faltings' proof of the Mordell Conjecture). This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required.

Industry Reviews

"A great subject and expert authors!"
Nieuw Archief voor Wiskunde, June 2001

"Both Eisenbud and Harris are experienced and compelling educators of modern mathematics. This book is strongly recommended to anyone who would like to know what schemes are all about."
Newsletter of the New Zealand Mathematical Society, No. 82, August 2001

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Non-Fiction Mathematics Geometry Algebraic Geometry

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Published: 1st January 2002

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Introduction	p. 1
Basic Definitions	p. 7
Affine Schemes	p. 7
Schemes in General	p. 21
Relative Schemes	p. 35
The Functor of Points	p. 42
Examples	p. 47
Reduced Schemes over Algebraically Closed Fields	p. 47
Reduced Schemes over Non-Algebraically Closed Fields	p. 53
Nonreduced Schemes	p. 57
Arithmetic Schemes	p. 81
Projective Schemes	p. 91
Attributes of Morphisms	p. 92
Proj of a Graded Ring	p. 95
Invariants of Projective Schemes	p. 124
Classical Constructions	p. 151
Flexes of Plane Curves	p. 151
Blow-ups	p. 162
Fano Schemes	p. 192
Forms	p. 204
Local Constructions	p. 209
Images	p. 209
Resultants	p. 222
Singular Schemes and Discriminants	p. 230
Dual Curves	p. 240
Double Point Loci	p. 246
Schemes and Functors	p. 251
The Functor of Points	p. 252
Characterization of a Space by its Functor of Points	p. 259
References	p. 279
Index	p. 285
Table of Contents provided by Blackwell. All Rights Reserved.

The Geometry of Schemes

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Hardcover

Industry Reviews

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How to return your order

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You Can Find This Book In

Other Editions and Formats

Paperback

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