What about Simon Donaldson's Riemann surfaces?

3.3k Views Asked by At

I am studying Riemann surfaces now. How about Donaldson's book "Riemann surfaces"? Could you recommend some references, and point out the required mathematical knowledge? Many thanks in advance!

1

There are 1 best solutions below

1
On BEST ANSWER

The answer depends on the topics you are interested in.

Unfortunately I do not know Donaldson's textbook, but I have found this reference

http://www2.imperial.ac.uk/~skdona/RSPREF.PDF

It is nice to see the chapter on "Elliptic Functions and integrals".

I personally recommend Farkas & Kra's "Riemann Surfaces" and Forster's "Lectures on Riemann Surfaces". The first book may have a bit old fashioned notation when it explains divisors, but it is a great text, with a lot of explicit computations and a great section on theta functions.

Both textbooks introduce the minimum amount of complex analysis which is needed to understand the theory of Riemann surfaces.

I would even have a look at the first chapters of Griffiths & Harris "Principles of Algebraic Geometry": they deal with complex geometry.