# 代數幾何 (書)

作者 Robin Hartshorne 英文 代數幾何 教科書 Springer-Verlag 1977 496 0-387-90244-9

## 目錄

Chapter I: Varieties

1. Affine Varieties
2. Projective Varieties
3. Morphisms
4. Rational Maps
5. Nonsingular Varieties
6. Nonsingular Curves
7. Intersections in Projective Space
8. What Is Algebraic Geometry?

Chapter IIː Schemes

1. Sheaves
2. Schemes
3. First Properties of Schemes
4. Separated and Proper Morhpisms
5. Sheaves of Modules
6. Divisors
7. Projective Morphisms
8. Differentials
9. Formal Schemes

Chapter IIIː Cohomology

1. Derived Functors
2. Cohomology of Sheaves
3. Cohomology of a Noetherian Affine Scheme
4. Cech Cohomology
5. The Cohomology of Projective Space
6. Ext Groups and Sheaves
7. The Serre Duality Theorem
8. Higher Direct Images of Scheaves
9. Flat Morphisms
10. Smooth Morphisms
11. The Theorem on Formal Functions
12. The Semicontinuity Theorem

Chapter IVː Curves

1. Riemann-Roch Theorem
2. Hurwitz's Theorem
3. Embeddings in Projective Space
4. Elliptic Curves
5. The Canonical Embedding
6. Classification of Curves in ${\displaystyle \mathbb {P} ^{3}}$

Chapter Vː Surfaces

1. Geometry on a Surface
2. Ruled Surfaces
3. Monoidal Transformations
4. The Cubic Surface in ${\displaystyle \mathbb {P} ^{3}}$
5. Birational Transformations
6. Classification of Surfaces

## 註

1. MathSciNet指出呢本書被人引用過超過2500次。

## 參考書

• Hartshorne, Robin (1977), Algebraic Geometry, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157, Zbl 0367.14001
• Shatz, Stephen S. (1979), "Review: Robin Hartshorne, Algebraic geometry", Bull. Amer. Math. Soc. (N.S.), 1 (3): 553–560, doi:10.1090/S0273-0979-1979-14618-4