The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics, 1358) [2nd exp. ed. 1999] 354063293X, 9783540632931

Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as

140 25 2MB

English Pages 304 [312] Year 1999

Table of contents :
Cover
LNM 1358
Title Page
Preface to the Second Edition
Preface to the First Edition
Table of Contents
I. Varieties
§1. Some algebra
§2. Irreducible algebraic sets
§3. Definition of a morphism
§4. Sheaves and affine varieties
§5. Definition of prevarieties and morphisms
§6. Products and the Hausdorff axiom
§7. Dimension
§8. The fibres of a morphism
§9. Complete varieties
§10. Complex varieties
II. Preschemes
§1. Spec (R)
§2. The category of preschemes
§3. Varieties and preschemes
§4. Fields of definition
§5. Closed subpreschemcs
§G. The functor of points of a prescheme
§7. Proper morphisms and finite morphisms
§8. Specialization
III. Local Properties of Schemes
§1. Quasi-coherent modules
§2. Coherent modules
§3. Tangent cones
§4. Non-singularity and differentials
§5. Etale morphisms
§6. Uniformizing parameters
§7. Non-singularity and the UFD property
§8. Normal varieties and normalization
§9. Zariski's Main Theorem
§10. Flat and smooth morphisms
Appendix: Curves and Their Jacobians
I. What is a Curve and How Explicitly Can We Describe Them
II. The Moduli Space of Curves: Definition, Coordinatization, and Some Properties
III. How Jacobians and Theta Functions Arise
IV. 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

The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians (Lecture Notes in Mathematics, 1358) [2nd exp. ed. 1999]
354063293X, 9783540632931

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