Riemann Surfaces and Algebraic Curves

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field in algebraic geometry. Designed for undergraduate study, this classroom-tested text demonstrates the connections between diverse areas of mathematics and features short essays by guest writers as well as over 100 exercises for the reader.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.