Riemann-Roch Spaces and Computation
Riemann-Roch Spaces and Computation
De Gruyter | Mathematics | March 2015 | ISBN-10: 3110426137 | 151 pages | epub | 5.4 mb
De Gruyter | Mathematics | March 2015 | ISBN-10: 3110426137 | 151 pages | epub | 5.4 mb
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.
Aims and Scope
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.
Topics
Algebra and Number Theory
Geometry and Topology
Numerical and Computational Mathematics
Applied Mathematics
TABLE OF CONTENTS
Frontmatter
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
More info and Hardcover at De Gruyter
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