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Riemann Surfaces$
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Simon Donaldson

Print publication date: 2011

Print ISBN-13: 9780198526391

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198526391.001.0001

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Meromorphic functions and the Main Theorem for compact Riemann surfaces

Meromorphic functions and the Main Theorem for compact Riemann surfaces

Chapter:
(p.110) (p.111) 8 Meromorphic functions and the Main Theorem for compact Riemann surfaces
Source:
Riemann Surfaces
Author(s):

Simon Donaldson

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198526391.003.0008

This chapter explains a strategy for proving the fundamental structural results about Riemann surfaces. It first considers the consequence of the Main Theorem for compact Riemann surfaces. It then analyzes the Riemann-Roch formula, the fundamental tool in the theory of compact Riemann surfaces.

Keywords:   Riemann surfaces, Riemann-Roch formula, Main Theorem

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