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Tables of Contents for The Red Book of Varieties and Schemes
Chapter/Section Title
Page #
Page Count
Preface to the Second Edition
V
2
Preface to the First Edition
VII
2
Table of Contents
IX
 
I. Varieties
1
64
1. Some algebra
1
4
2. Irreducible algebraic sets
5
6
3. Definition of a morphism
11
5
4. Sheaves and affine varieties
16
9
5. Definition of prevarieties and morphisms
25
8
6. Products and the Hausdorff Axiom
33
7
7. Dimension
40
8
8. The fibres of a morphism
48
6
9. Complete varieties
54
3
10. Complex varieties
57
8
II. Preschemes
65
72
1. Spec (R)
66
11
2. The category of preschemes
77
9
3. Varieties and preschemes
86
8
4. Fields of definition
94
9
5. Closed subpreschemes
103
9
6. The functor of points of a prescheme
112
9
7. Proper morphisms and finite morphisms
121
6
8. Specialization
127
10
III. Local Properties of Schemes
137
88
1. Quasi-coherent modules
138
8
2. Coherent modules
146
7
3. Tangent cones
153
11
4. Non-singularity and differentials
164
10
5. Etale morphisms
174
9
6. Uniformizing parameters
183
4
7. Non-singularity and the UFD property
187
9
8. Normal varieties and normalization
196
11
9. Zariski's Main Theorem
207
7
10. Flat and smooth morphisms
214
11
Appendix: Curves and Their Jacobians
225
68
Lecture I: What is a Curve and How Explicitly Can We Describe Them?
229
14
Lecture II: The Moduli Space of Curves: Definition, Coordinatization, and Some Properties
243
14
Lecture III: How Jacobians and Theta Functions Arise
257
14
Lecture IV: The Torelli Theorem and the Schottky Problem
271
16
Survey of Work on the Schottky Problem up to 1996 by Enrico Arbarello
287
6
References: The Red Book of Varieties and Schemes
293
1
Guide to the Literature and References: Curves and Their Jacobians
294
7
Supplementary Bibliography on the Schottky Problem
301
 
Enrico Arbarello
List of Figures and Tables
ix
2
Acknowledgments
xi
 
Introduction
1
9
1 An Ethnic Economy
10
23
2 A Family Affair
33
21
3 Starting Out in the Thirties
54
26
4 The Landscape of Jewish Life
80
23
5 From Neighborhood to New Deal
103
33
6 Private Jewish Philanthropy in the Welfare State
136
30
7 The Spiritual Depression
166
31
8 American Jews and the American Dream
197
10
Appendix
207
4
Abbreviations
211
2
Notes
213
48
Index
261