Compact Riemann surfaces = 紧黎曼曲面 /
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ISBN：9787510027390
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简介
《紧黎曼曲面》内容简介：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 serre\'s original paper）, thepresent notes follow dr. stadler\'s fairly closely.
目录
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
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
Compact Riemann surfaces = 紧黎曼曲面 /
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