紧黎曼曲面 英文PDF电子书下载

本书以ETH讲义为基础编写而成，旨在介绍函数理论和紧黎曼曲面的基本知识。书中用层论方法，向量丛和Srre对偶定理介绍了Riemann-Roch定理，并将其运用在射影空间中代数曲线的几何和紧黎曼曲面和Jacaboan定理关系的研究中。

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1．Algebraic functions 3

2．Riemann surfaces 8

3．The sheaf of germs of holomorphic functions 12

4．The Riemann surface of an algebraic function 15

5．Sheaves 17

6．Vector bundles,line bundles and divisors 27

7．Finiteness theorems 32

8．The Dolbeault isomorphism 38

9．Weyl's lemma and the Serre duality theorem 43

10．The Riemann-Roch theorem and some applications 49

11．Further properties of compact Riemann surfaces 58

12．Hyperelliptic curves and the canonical map 63

13．Some geometry of curves in projective space 66

14．Bilinear relations 77

15．The Jacobian and Abel's theorem 84

16．The Riemann theta function 91

17．The theta divisor 97

18．Torelli's theorem 106

19．Riemann's theorem on the singularities of θ 111

References 119

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