Description

Book Synopsis
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.

Trade Review
"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

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

Introduction to Compact Riemann Surfaces and Dessins dEnfants 79 London Mathematical Society Student Texts Series Number 79

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    A Paperback by Ernesto Girondo, Gabino González-Diez

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      View other formats and editions of Introduction to Compact Riemann Surfaces and Dessins dEnfants 79 London Mathematical Society Student Texts Series Number 79 by Ernesto Girondo

      Publisher: Cambridge University Press
      Publication Date: 12/22/2011 12:00:00 AM
      ISBN13: 9780521740227, 978-0521740227
      ISBN10: 0521740223
      Also in:
      Algebraic topology Complex analysis, complex variables

      Description

      Book Synopsis
      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.

      Trade Review
      "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

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

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