<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically 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 paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces.</p>
</abstract>

The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically 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 paper is to give two proofs of this important theorem and explore some of its numerous consequences. As an application, we compute the genus of some interesting algebraic curves or Riemann surfaces.

Riemann-Roch theorem and Kodaira-Serre duality

Department of Mathematics, Faculty of Sciences

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Riemann-Roch theorem and Kodaira-Serre duality"}

The Riemann-Roch theorem is of utmost importance and a vital tool to the fields of complex analysis and algebraic geometry, specifically in the algebraic...

Riemann-Roch theorem and Kodaira-Serre duality

Published Online: Jun 20, 2022

Page range: 4 - 17

DOI: https://doi.org/10.2478/awutm-2022-0002

Keywords
Riemann surfaces, curves, Riemann-Roch theorem

© 2022 A. Lesfari, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Riemann-Roch theorem and Kodaira-Serre duality

Published Online: Jun 20, 2022

Page range: 4 - 17

DOI: https://doi.org/10.2478/awutm-2022-0002

KeywordsRiemann surfaces, curves, Riemann-Roch theorem

© 2022 A. Lesfari, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Riemann surfaces, curves, Riemann-Roch theorem