Introduction to Compact Riemann Surfaces and Dessins d-Enfants PDF (Adobe DRM) download by Ernesto Girondo

Introduction to Compact Riemann Surfaces and Dessins d-Enfants

Cambridge University Press
Publication date: December 2011
ISBN: 9781139200127
Digital Book format: PDF (Adobe DRM)

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Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.
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