代數幾何 (書)

代數幾何係一本好有影響力嘅代數幾何教科書，喺1977年由Robin Hartshorne寫，Springer-Verlag出版。

影響力 
佢係第一本寫畀研究生睇，詳細介紹概形論嘅教科書。喺香港嚟講，科大李衛平教授教嘅代數幾何課程都係用呢本書。

內容 
第一課標題係「簇」，主要講經典嘅代數封閉場上嘅代數簇理論，呢課用咗好多交換代數入面嘅定理，例如Hilbert's Nullstellensatz，主要目錄 

Chapter I: Varieties
 Affine Varieties
 Projective Varieties
 Morphisms
 Rational Maps
 Nonsingular Varieties
 Nonsingular Curves
 Intersections in Projective Space
 What Is Algebraic Geometry?

Chapter IIː Schemes
 Sheaves
 Schemes
 First Properties of Schemes
 Separated and Proper Morhpisms
 Sheaves of Modules
 Divisors
 Projective Morphisms
 Differentials
 Formal Schemes

Chapter IIIː Cohomology
 Derived Functors
 Cohomology of Sheaves
 Cohomology of a Noetherian Affine Scheme
 Cech Cohomology
 The Cohomology of Projective Space
 Ext Groups and Sheaves
 The Serre Duality Theorem
 Higher Direct Images of Scheaves
 Flat Morphisms
 Smooth Morphisms
 The Theorem on Formal Functions
 The Semicontinuity Theorem

Chapter IVː Curves
 Riemann-Roch Theorem
 Hurwitz's Theorem
 Embeddings in Projective Space
 Elliptic Curves
 The Canonical Embedding
 Classification of Curves in 

Chapter Vː Surfaces
 Geometry on a Surface
 Ruled Surfaces
 Monoidal Transformations
 The Cubic Surface in 
 Birational Transformations
 Classification of Surfaces

參考書 

數學教科書
1977年嘅書
代數幾何