Riemann-Roch spaces and computation / Paraskevas Alvanos.

Format:

Book

Author/Creator:

Alvanos, Paraskevas, author.

Language:

English

Subjects (All):

Riemann surfaces.

Physical Description:

1 online resource (151 pages)

Edition:

1st ed.

Place of Publication:

Warsaw, [Poland] ; Berlin, [Germany] : De Gruyter Open, 2014.

Language Note:

English

Summary:

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.

Contents:

Front matter

Contents

Preface

Part I: Riemann-Roch Spaces

1 Elements of Algebra

2 Function Fields and Curves

3 Riemann-Roch Spaces

4 Integral Domains

Part II: Computation

5 Computing Integral Bases

6 Computing Riemann-Roch Spaces

7 Computing Resultant and Norm Form Equations

8 Computing Integral Points on Rational Curves

Appendices

Bibliography

Index

Index of Algorithms

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

This eBook is made available Open Access. Unless otherwise specified individually in the content, the work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license: https://creativecommons.org/licenses/by-nc-nd/3.0 https://www.degruyter.com/dg/page/open-access-policy

Description based on online resource; title from PDF title page (ebrary, viewed May 28, 2015).

ISBN:

3-11-043948-4

3-11-042612-9

OCLC:

1002264468