Riemann-Roch Spaces and Computation

Paraskevas Alvanos

Open Access Published by De Gruyter Open Poland 2015

Riemann-Roch Spaces and Computation

Paraskevas Alvanos

https://doi.org/10.2478/9783110426120

Overview
Contents

About this book

The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important, a variety of examples with codes of algorithms are given in the book, covering the majority of the cases.

Author / Editor information

Paraskevas Alvanos, Model Experimental High School of Thessaloniki, Greece

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Preface Publicly Available Download PDF	VIII
Part I: Riemann-Roch Spaces
1 Elements of Algebra Publicly Available Download PDF	2
2 Function Fields and Curves Publicly Available Download PDF	17
3 Riemann-Roch Spaces Publicly Available Download PDF	32
4 Integral Domains Publicly Available Download PDF	44
Part II: Computation
5 Computing Integral Bases Publicly Available Download PDF	54
6 Computing Riemann-Roch Spaces Publicly Available Download PDF	73
7 Computing Resultant and Norm Form Equations Publicly Available Download PDF	85
8 Computing Integral Points on Rational Curves Publicly Available Download PDF	98
Appendices Publicly Available Download PDF	115
Bibliography Publicly Available Download PDF	136
Index Publicly Available Download PDF	139
Index of Algorithms Publicly Available Download PDF	141

(Deutsch)

Language: English
Publisher: De Gruyter Open Poland
Audience: Researchers and graduate students in algebraic geometry and number theory.
Pages
- Main content: 151
Illustrations
- Illustrations: 1
- Coloured Illustrations: 3
- Tables: 7
Keywords: Riemann-Roch spaces; Diophantine equations; integral domains

eBook

Published: March 11, 2015
ISBN: 9783110426120

Hardcover

Published: March 26, 2015
ISBN: 9783110426137