Riemann Surfaces and Algebraic Curves

A First Course in Hurwitz Theory

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Riemann Surfaces and Algebraic Curves by Renzo Cavalieri, Eric Miles, Cambridge University Press
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Author: Renzo Cavalieri, Eric Miles ISBN: 9781316798669
Publisher: Cambridge University Press Publication: September 26, 2016
Imprint: Cambridge University Press Language: English
Author: Renzo Cavalieri, Eric Miles
ISBN: 9781316798669
Publisher: Cambridge University Press
Publication: September 26, 2016
Imprint: Cambridge University Press
Language: English

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 the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

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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 the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

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