代數幾何原理（簡體書）

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.

第O章　基礎知識
1.多復變初步
柯西公式及應用
多變量
魏爾斯特拉斯定理及其推論
解析簇
2.復流形
復流形
子流形與子簇
De Rham和DoIbeault上同調
復流形上的積分
3.層和上同調
起源：米塔-列夫勒問題
層
層的上同調
De Rham定理
Colbeault定理
4.流形的拓撲
閉鏈的相交
龐加萊對偶
解析閉鏈的相交
5.向量叢、聯絡和曲率
全純復向量叢
度量、聯絡和曲率
6.緊致復流形的調和理論
霍奇定理
霍奇定理I的證明——局部理論
霍奇定理II的證明——全局理論
霍奇定理的應用
7.Kahler流形
Kahler條件
霍奇恆等式和霍奇分解
Lefschetz分解
第1章　復代數簇
　1.除子與線叢
除子
線叢
線叢的陳類
　2.消滅定理及推論
小平消滅定理
超平面截面的Lefschetz定理
定理
（1，1）類的Lefschetz定理
　3.代數簇
解析簇和代數簇
簇的次數
代數簇的切空間
4.小平嵌入定理
線叢和到投影空間的映射
脹開
小平定理的證明
5.格拉斯曼理論
定義
胞腔分解
Schubert微積分
萬有叢
Plucker嵌入
第2章　Riemann曲面和代數曲線
第3章　深入技巧
第4章　曲面
第5章　留數
第6章　二次線叢
索引