《代数几何原理》主要内容：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.
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代数几何初步
评分Mittag–Leffler 问题和狄利克雷问题形式等价。本书主旨是利用除子或是线丛来表达曲线和曲面问题，而高维利用对偶定理得到。局部留数定理来自柯西积分公式，而整体留数则来自子流形的对偶stokes公式。留数的分析定义来自积分还可以从上同调类理解。lef固定点定理和博特留数公式都是依据流相交和光滑理论退化到奇异微分形式（B-M的核-偏微分基本解-隐含着对偶-酉不变-整体公式-黎曼罗赫定理和托德多项式）黎曼罗赫定理其实低维对应就是实系数二次三次方程的解的判别式的高维推广，陈类一方面表示了除子携带的基本同调闭链的庞加莱对偶 另一方面 德拉姆上同调中线丛中的任意联络的曲率给出。在层论中的serre对偶定理等价于流形拓扑中的庞加莱对偶定理
评分griffiths得到08年度的wolf prize
评分买得这本书都被翻得黑得不成样了，感觉这书读起来还是挺顺的，比较容易把握要点
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