The Riemann Roch Theorem (for algebraic curves)

Date

2017

Authors

Zheng, Weiqiong

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

The Riemann-Roch theorem is a useful tool to calculate the dimension of the space of meromorphic functions with prescribed zeros and poles. There are severals versions of the theorem such as the Riemann-Roch theorem for line bundles, for (algebraic) curves, for surfaces and for higher dimensions. In this thesis, we will focus on the Riemann-Roch theorem for algebraic curves over an algebraically closed eld, which is a very important result in complex analysis and algebraic geometry. The study of the elds of rational functions on curves can be very useful in the proof. So we will recall some pre-knowledges in commutative algebra and some facts about a ne varieties. Then talk about function elds, discrete valuation rings and Weil di erentials to prove the theorem, using the methods of Andre Weil.

Description

Keywords

Citation

Source

Type

Thesis (Honours)

Book Title

Entity type

Access Statement

License Rights

DOI

10.25911/5d9efb990f3b8

Restricted until