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Riemann Surfaces and Algebraic Curves : A First Course in Hurwitz Theory

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"Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and  Read more...

Author(s): Cavalieri, Renzo; Miles, Eric W.
Series: London Mathematical Society student texts 87
Publisher: Cambridge University Press
Year: 2016

Language: English
Pages: 183
City: New York
Tags: Riemann surfaces;Curves, Algebraic;Geometry, Algebraic

Introduction
1. From complex analysis to Riemann surfaces
2. Introduction to manifolds
3. Riemann surfaces
4. Maps of Riemann surfaces
5. Loops and lifts
6. Counting maps
7. Counting monodromy representations
8. Representation theory of Sd
9. Hurwitz numbers and Z(Sd)
10. The Hurwitz potential
Appendix A. Hurwitz theory in positive characteristic
Appendix B. Tropical Hurwitz numbers
Appendix C. Hurwitz spaces
Appendix D. Does physics have anything to say about Hurwitz numbers?
References
Index.