Fall 2004

221 U0790 Riemann Surfaces 黎曼面

Homework:

HW1 HW2 HW3 HW4

Course Information

Instructor : Jungkai Chen陳榮凱

Place: New Math Bldg 405

Hours: Fri. 2,3,4

First meeting: Sep 17. 2004.

一.內容：

1. Riemann surface

2. Sheaves

3. Vector bundles, line bundles and divisors

4. Dolbeault`s theorem

5. Serre duality

6. Riemann-Roch theorem

7. Canonical maps

8. Bilinear relation

9. Jacobian and Abel’s theorem

10. Theta function and theta divisor

11. Torelli`s theorem

12. Singularieties of theta divisor

13. Schottky problem

二.參考書（教科書）：

1. Narasimhan, R. : Compact Riemann Surfaces, 1992, Birkhauser Verlag

2. Foster, O.: Lectures on Riemann Surfaces, GTM 81, 1981, Springer Verlag

3. Mumfor, D.: Curves and their Jacobian, 1975. See also in appendix of: The Red Book of Varieties and Schemes, 2nd ed., LNM 1358, 1999, Springer Verlag

4. Clemens, H.: A Scrapbook of Complex Curve Theory, GSM 55, 2002, Amer. Math. Soc.

三. 成績評量方式：

1. homework: 30 %

2. term paper: 50 %

3. participation: 20 %