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

ISBN-10: 354063293X

ISBN-13: 9783540632931

Edition: 2nd 1999 (Revised)

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Description: Mumford's famous Red Bookgives 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 learn i) 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.

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Book details

List price: $74.95
Edition: 2nd
Copyright year: 1999
Publisher: Springer
Publication date: 9/17/1999
Binding: Paperback
Pages: 314
Size: 5.75" wide x 8.75" long x 0.75" tall
Weight: 0.946
Language: English

Preface to the Second Edition
Preface to the First Edition
Varieties
Some algebra
Irreducible algebraic sets
Definition of a morphism
Sheaves and affi ne varieties
Definition of prevarieties and morphisms
Products and the Hausdorff Axiom
Dimension
The fibres of a morphism
Complete varieties
Complex varieties
Preschemes
Spec (R)
The category of preschemes
Varieties and preschemes
Fields of definition
Closed subpreschemes
The functor of points of a prescheme
Proper morphisms and finite morphisms
Specialization
Local Properties of Schemes
Quasi-coherent modules
Coherent modules
Tangent cones
Non-singularity and differentials
�tale morphisms
Uniformizing parameters
Non-singularity and the UFD property
Normal varieties and normalization
Zariski's Main Theorem
Flat and smooth morphisms
Appendix: Curves and Their Jacobians
What is a Curve and How Explicitly Can We Describe Them?
The Moduli Space of Curves: Definition, Coordinatization, and Some Properties
How Jacobians and Theta Functions Arise
The Torelli Theorem and the Schottky Problem
Survey of Work on the Schottky Problem up to 1996 by Enrico Arbarello
References: The Red Book of Varieties and Schemes
Guide to the Literature and References: Curves and Their Jacobians
Supplementary Bibliography on the Schottky Problem by Enrico Arbarello
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