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The Red Book of Varieties and Schemes : Includes the Michigan Lectures (1974) on Curves and Their Jacobians :  Includes the Michigan Lectures (1974) on Curves and Their Jacobians - David Mumford

The Red Book of Varieties and Schemes : Includes the Michigan Lectures (1974) on Curves and Their Jacobians

Includes the Michigan Lectures (1974) on Curves and Their Jacobians

Paperback

Published: October 1999
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Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about. This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learni) the concept of "scheme" as part of their study of algebraic geometry and ii) an overview of moduli problems for curves and of the use of theta functions to study these.

"This is the second edition of a famous and well-known introduction to algebraic geometry, written to show that the language of schemes is fundamentally geometrical and clearly expressing the intuition of algebraic geometry. ... This book can strongly be recommended to anybody interested in algebraic geometry and willing to learn about varieties and schemes and their main problems."
EMS Newsletter, Vol. 37, Sept. 2000

Preface to the Second Editionp. v
Preface to the First Editionp. vii
Varietiesp. 1
Some algebrap. 1
Irreducible algebraic setsp. 5
Definition of a morphismp. 11
Sheaves and affi ne varietiesp. 16
Definition of prevarieties and morphismsp. 25
Products and the Hausdorff Axiomp. 33
Dimensionp. 40
The fibres of a morphismp. 48
Complete varietiesp. 54
Complex varietiesp. 57
Preschemesp. 65
Spec (R)p. 66
The category of preschemesp. 77
Varieties and preschemesp. 86
Fields of definitionp. 94
Closed subpreschemesp. 103
The functor of points of a preschemep. 112
Proper morphisms and finite morphismsp. 121
Specializationp. 127
Local Properties of Schemesp. 137
Quasi-coherent modulesp. 138
Coherent modulesp. 146
Tangent conesp. 153
Non-singularity and differentialsp. 164
√Čtale morphismsp. 174
Uniformizing parametersp. 183
Non-singularity and the UFD propertyp. 187
Normal varieties and normalizationp. 196
Zariski's Main Theoremp. 207
Flat and smooth morphismsp. 214
Appendix: Curves and Their Jacobiansp. 225
What is a Curve and How Explicitly Can We Describe Them?p. 229
The Moduli Space of Curves: Definition, Coordinatization, and Some Propertiesp. 243
How Jacobians and Theta Functions Arisep. 257
The Torelli Theorem and the Schottky Problemp. 271
Survey of Work on the Schottky Problem up to 1996 by Enrico Arbarellop. 287
References: The Red Book of Varieties and Schemesp. 293
Guide to the Literature and References: Curves and Their Jacobiansp. 294
Supplementary Bibliography on the Schottky Problem by Enrico Arbarellop. 301
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540632931
ISBN-10: 354063293X
Series: Red Book of Varieties & Schemes : Book 1358
Audience: General
Format: Paperback
Language: English
Number Of Pages: 314
Published: October 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: US
Dimensions (cm): 23.4 x 15.4  x 1.8
Weight (kg): 0.48
Edition Number: 2
Edition Type: Revised