Introduction to Compact Riemann Surfaces and Dessins d’Enfants

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Ernesto Girondo (Universidad Autónoma de Madrid) Gabino González-Diez (Universidad Autónoma de Madrid)

Introduction to Compact Riemann Surfaces and Dessins d’Enfants

Ernesto Girondo (Universidad Autónoma de Madrid), Gabino González-Diez (Universidad Autónoma de Madrid)

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English

Cambridge University Press
22 December 2011

Mathematics & Sciences; Complex analysis, complex variables; Algebraic topology

Series: London Mathematical Society Student Texts

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 2011 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.

By: Ernesto Girondo (Universidad Autónoma de Madrid), Gabino González-Diez (Universidad Autónoma de Madrid)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 79
Dimensions: Height: 228mm, Width: 153mm, Spine: 16mm
Weight: 460g
ISBN: 9780521740227
ISBN 10: 0521740223
Series: London Mathematical Society Student Texts
Pages: 310
Publication Date: 22 December 2011
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Riemann surfaces and algebraic curves; 2. Riemann surfaces and Fuchsian groups; 3. Belyi's theorem; 4. Dessins d'enfants; References; Index.

Ernesto Girondo is Profesor Titular de Geometria y Topologia in the Department of Mathematics at Universidad Autonoma de Madrid. Gabino Gonzalez-Diez is Catedratico de Geometria y Topologia in the Department of Mathematics at Universidad Autonoma de Madrid.

Reviews for Introduction to Compact Riemann Surfaces and Dessins d’Enfants

Overall the text is very well written and easy to follow, partly due to the abundance of good concrete examples in every single section illustrating concepts from the very basic to the very technical. Aaron D. Wootton, Mathematical Reviews