Is there any good reference on Riemann Surface and Riemann Theta Function?

[yicong2011]

Hi,

Currently, I need to read some reference about Integrable System, but I am stuck in Riemann Surface, genus, divisors, and Riemann Theta Functions. This makes me anxious.

Is there introduction or pedagogical reference on this topic? I think I can spend some time read it during winter vacation.

Thank you very much. Enjoy your Thanksgiving.

 

[mathwonk]

I learned a lot from chapter 2 of Algebraic geometry, by Griffiths and Harris.

There was also a "college on riemann surfaces" at the ICTP in 1987 that may be useful,

'Lectures on Riemann surfaces
proceedings of the College on Riemann Surfaces, International Centre for Theoretical Physics, Trieste, Italy, 9 Nov.-18 Dec., 1987
editors, M. Cornalba, X. Gomez-Mont, A. Verjovsky.
Published 1989 by World Scientific in Singapore, Teaneck, NJ .
Written in English.

 

[mathwonk]

here is a quick sketch. the theta divisor mentioned on the last page is the zero locus of Riemann's theta function.