緊黎曼曲面

內(nèi)容概要

These notes form the contents of a Nachdiplomvorlesung given at the Forschungs-institut f/ir Mathematik of the EidgenSssische Technische Hochschule, Ziirich from November, 1984 to February, 1985. Prof. K. Chandrasekharan and Prof. J/irgen Moser have encouraged me to write them up for inclusion in the series, published by Birkhauser, of notes of these courses at the ETH.

書籍目錄

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. hypereuiptic 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

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