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!
2026-03-31 22:45:33.1774997133
What about Simon Donaldson's Riemann surfaces?
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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.