代数几何原理英文版

　　A third general principle was that this volume should be stir-contained.In particular any "hard" result that would be utilized should be fullyproved. A difficulty a student often faces in a subject as diverse as algebraic geometry is the profusion of cross-references， and this is one reason for attempting to be self-contained. Similarly， we have attempted to avoid allusions to， or statements without proofs of， related results. This book is in no way meant to be a survey of algebraic geometry， but rather is designed to develop a working facility with specific geometric questions.Our approach to the subject is initially analytic： Chapters 0 and 1 treat the basic techniques and results of complex manifold theory， with some emphasis on results applicable to projective varieties. Beginning in Chapter 2 with the theory of Riemann surfaces and algebraic curves， and continu-ing in Chapters 4 and 6 on algebraic surfaces and the quadric line complex， our treatment becomes increasingly geometric along classicallines. Chapters 3 and 5 continue the analytic approach， progressing to more special topics in complex manifolds.

暂缺《代数几何原理英文版》作者简介

第O章　基础知识
1.多复变初步
　　柯西公式及应用
多变量
魏尔斯特拉斯定理及其推论
解析簇
2.复流形
复流形
子流形与子簇
De Rham和DoIbeault上同调
复流形上的积分
3.层和上同调
起源：米塔-列夫勒问题
层
层的上同调
De Rham定理
Colbeault定理
4.流形的拓扑
闭链的相交
庞加莱对偶
解析闭链的相交
5.向量丛、联络和曲率
全纯复向量丛
度量、联络和曲率
6.紧致复流形的调和理论
霍奇定理
霍奇定理I的证明——局部理论
霍奇定理II的证明——全局理论
霍奇定理的应用
7.Kahler流形
Kahler条件
霍奇恒等式和霍奇分解
Lefschetz分解
第1章　复代数簇
　1.除子与线丛
除子
线丛
线丛的陈类
　2.消灭定理及推论
小平消灭定理
超平面截面的Lefschetz定理
定理
（1，1）类的Lefschetz定理
　3.代数簇
解析簇和代数簇
簇的次数
代数簇的切空间
4.小平嵌入定理
线丛和到投影空间的映射
胀开
小平定理的证明
5.格拉斯曼理论
定义
胞腔分解
Schubert微积分
万有丛
Plucker嵌入
第2章　Riemann曲面和代数曲线
第3章　深入技巧
第4章　曲面
第5章　留数
第6章　二次线丛
索引