TY  - GEN
AU  - Mumford, David
TI  - The red book of varieties and schemes: : includes the Michigan Lectures (1974) on curves and their Jacobians
SN  - 354063293X
U1  - 516.35 
PY  - 1999///
CY  - Berlin
PB  - Springer
KW  - Algebraic Geometry
KW  - Mathematics
N1  - 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
ER  -