Le théorème de Riemann-Roch et ses applications

Details Le théorème de Riemann-Roch et ses applications Le théorème de Riemann-Roch et ses applications

2007-06-18

arxiv.org/abs/0706.2673v1

Mathematics

Complex Variables

16 pages

Scientific paper

The Riemann-Roch theorem is of utmost importance in the algebraic geometric theory of compact Riemann surfaces. It tells us how many linearly independent meromorphic functions there are having certain restrictions on their poles. The aim of this article is to present a simple direct proof of this theorem and explore some of its numerous consequences. We also give an analytic proof of the Riemann-Hurwitz formula. As an application, we compute the genus of some interesting algebraic curves.

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