这本《紧黎曼曲面》由美国Raghavan Narasimhan所著，内容是：These notes form the contents of a Nachdiplomvorlesung given at the Forschungs-institut ffir Mathematik of the Eidgen5ssische Technische Hochschule, Zfirich from November, 1984 to February, 1985. Prof. K. Chandrasekharan and Prof. Jiirgen Moser have encouraged me to write them up for inclusion in the series, published by Birkhauser, of notes of these courses at the ETH.

1. Algebraic functions

2. Riemann surfaces

3. The sheaf of germs of holomorphic functions

4. The Riemann surface of an algebraic function

5. Sheaves

6. Vector bundles, line bundles and divisors

7. Finiteness theorems

8. The Dolbeault isomorphism

9. Weyl's lemma and the Serre duality theorem

10. The Riemann-Roch theorem and some applications

11. Further properties of compact Riemann surfaces

12. Hyperelliptic curves and the canonical map

13. Some geometry of curves in projective space

14. Bilinear relations

15. The Jacobian and Abel's theorem

16. The Riemann theta function

17. The theta divisor

18. Torelli's theorem

19. Riemann's theorem on the singularities of θ

References