紧黎曼曲面

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. weyls lemma and the serre duality theorem

10. the riemann-roch theorem and some applications

11. further properties of compact riemann surfaces

12. hypereuiptic curves and the canonical map

13. some geometry of curves in projective space

14. bilinear relations

15. the jacobian and abels theorem

16. the riemann theta function

17. the theta divisor

18. torellis theorem

19. riemanns theorem on the singularities of θ

references

These notes form the contents of a Nachdiplomvorlesung given at the Forschungs-institut fiir Mathematik of the Eidgen6ssische Technische Hochschule， Ziirich fromNovember， 1984 to February， 1985. Prof. K. Chandrasekharan and Prof. JiirgenMoser have encouraged me to write them up for inclusion in the series， published byBirkhnser， of notes of these courses at the ETH.
Dr. Albert Stadler produced detailed notes of the first part of this course， and veryintelligible class-room notes of the rest. Without this work of Dr. StUrdier， these noteswould not have been written. While I have changed some things （such as the proof ofthe Serre duality theorem， here done entirely in the spirit of Serres original paper）， thepresent notes follow Dr. Stadlers fairly closely.