different proofs of the fact that compact riemann surface has a non-trivial meromorphic function

Asked Sep 18 '14 at 11:34

Active Sep 18 '14 at 11:39

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I would have like to have a list of different proofs of the fact that compact riemann surface has a non-trivial meromorphic function.This is certainly one of the main results of compact riemann surface.Some proofs use sheaves and some more elementary just using forms and some using riemann-roch theorem.

edited Sep 18 '14 at 11:39

asked Sep 18 '14 at 11:34

Koushik

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Related http://mathoverflow.net/questions/19649/physical-construction-of-nonconstant-meromorphic-functions-on-compact-riemann?rq=1 – David E Speyer Sep 18 '14 at 15:02

different proofs of the fact that compact riemann surface has a non-trivial meromorphic function

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