緊黎曼曲面(簡體書)

《緊黎曼曲面》內容簡介：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.本書以ETH講義為基礎編寫而成，旨在介紹函數理論和緊黎曼曲面的基本知識。書中用層論方法，向量叢和Srre對偶定理介紹了Riemann-Roch定理，並將其運用在射影空間中代數曲線的幾何和緊黎曼曲面和Jacaboan定理關係的研究中。本書的後半部分盡可能用Riemann自己經典論文的方法證明Abelian函數，表明Riemann方法和許多近代作者介紹該科目的方法沒有很大的區別。目次：代數函數；黎曼曲面；全純函數的芽層；代數函數的黎曼曲面；層論；向量叢、線叢和除子；有限性定理；Dolbeault同構；Wayl引理和Serre對偶定理；Riemann-Roch定理和應用；緊黎曼曲面的更多性質；超橢圓曲線和典範曲面；射影空間中的一些曲線幾何；雙線性關係；Jacobian和Abel定理；黎曼Theta函數；Theta除子；Torelli定理；Θ奇性的黎曼定理。
讀者對象：適用于數學專業的學生、老師和相關人員。

作者：（美國）納拉辛漢（Raghavan Narasimhan）

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
References