本书是沙法列维奇代数几何基础教程的第2卷。本书作者是当代著名的苏联/俄罗斯代数几何学家，是一位有独创性，知识极为渊博的数学家。作者的代数几何基础教程问世（俄文版1972年初版，英文版1977年初版）40多年来，一直被视为一部重要的代数几何经典名著。与同类书相比，本书内容全面，详尽，注重给出抽象理论的几何背景和起源，并配有充分反映几何本质的实例和图解。本书所需预备知识仅限于代数基础，是高年级本科生和研究生学习代数几何的首选教材。

Book 2: Schemes and Varieties
5 Schemes
1 The Spec of a Ring
1.1 Definition of Spec A
1.2 Properties of Points of Spec A
1.3 The Zariski Topology of Spec A
1.4 Irreducibility, Dimension
1.5 Exercises to Section 1
2 Sheaves
2.1 Presheaves
2.2 The Structure Presheaf
2.3 Sheaves
2.4 Stalks of a Sheaf
2.5 Exercises to Section 2
3 Schemes
3.1 Definition of a Scheme
3.2 Glueing Schemes
3.3 Closed Subschemes
3.4 Reduced Schemes and Nilpotents
3.5 Finiteness Conditions
3.6 Exercises to Section 3
4 Products of Schemes
4.1 Definition of Product
4.2 Group Schemes
4.3 Separatedness
4.4 Exercises to Section 4
6 Varieties
1 Definitions and Examples
1.1 Definitions
1.2 Vector Bundles
1.3 Vector Bundles and Sheaves
1.4 Divisors and Line Bundles
1.5 Exercises to Section 1
2 Abstract and Quasiprojective Varieties
2.1 Chow's Lemma
2.2 Blowup Along a Subvariety
2.3 Example of Non-quasiprojective Variety
2.4 Criterions for Projectivity
2.5 Exercises to Section 2
3 Coherent Sheaves
3.1 Sheaves of Ox-Modules
3.2 Coherent Sheaves
3.3 Dévissage of Coherent Sheaves
3.4 The Finiteness Theorem
3.5 Exercises to Section 3
4 Classification of Geometric Objects and Universal Schemes
4.1 Schemes and Functors
4.2 The Hilbert Polynomial
4.3 Flat Families
4.4 The Hilbert Scheme
4.5 Exercises to Section 4
Book 3: Complex Algebraic Varieties and Complex Manifolds
7 The Topology of Algebraic Varieties
1 The Complex Topology
1.1 Definitions
1.2 Algebraic Varieties as Differentiable Manifolds; Orientation
1.3 Homology of Nonsingular Projective Varieties
1.4 Exercises to Section 1
2 Connectedness
2.1 Preliminary Lemmas
2.2 The First Proof of the Main Theorem
2.3 The Second Proof
2.4 Analytic Lemmas
2.5 Connectedness of Fibres
2.6 Exercises to Section 2
3 The Topology of Algebraic Curves
3.1 Local Structure of Morphisms
3.2 Triangulation of Curves
3.3 Topological Classification of Curves
3.4 Combinatorial Classification of Surfaces
3.5 The Topology of Singularities of Plane Curves
3.6 Exercises to Section 3
……
Book 1: Varieties in Projective Space
References
Index