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The red book of varieties and schemes : includes the Michigan Lectures (1974) on Curves and their Jacobinians

Author: David Mumford
Publisher: Berlin ; New York : Springer, ©1999.
Series: Lecture notes in mathematics (Springer-Verlag), 1358.
Edition/Format:   Print book : English : 2nd expanded edView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David Mumford
ISBN: 354063293X 9783540632931
OCLC Number: 969857493
Description: x, 304 pages : illustrations ; 24 cm.
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 subpreschemes --
6. 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 --
App. Curves and Their Jacobians --
Lecture I. What is a Curve and How Explicitly Can We Describe Them? --
Lecture II. The Moduli Space of Curves: Definition, Coordinatization, and Some Properties --
Lecture III. How Jacobians and Theta Functions Arise --
Lecture IV. The Torelli Theorem and the Schottky Problem --
Survey of Work on the Schottky Problem up to 1996 / 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 / Enrico Arbarello.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1358.
Responsibility: David Mumford.
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