Preface to the Second Edition |
Preface to the First Edition |
Varieties / I: |
Some algebra / 1: |
Irreducible algebraic sets / 2: |
Definition of a morphism / 3: |
Sheaves and affi ne varieties / 4: |
Definition of prevarieties and morphisms / 5: |
Products and the Hausdorff Axiom / 6: |
Dimension / 7: |
The fibres of a morphism / 8: |
Complete varieties / 9: |
Complex varieties / 10: |
Preschemes / II: |
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 / III: |
Quasi-coherent modules |
Coherent modules |
Tangent cones |
Non-singularity and differentials |
Étale 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? / Lecture I: |
The Moduli Space of Curves: Definition, Coordinatization, and Some Properties / Lecture II: |
How Jacobians and Theta Functions Arise / Lecture III: |
The Torelli Theorem and the Schottky Problem / Lecture IV: |
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 |
Preface to the Second Edition |
Preface to the First Edition |
Varieties / I: |