Introduction to Compact Riemann Surfaces and Dessins d'Enfants

Erscheinungsjahr 2011
ISBN: 978-0-521-74022-7
Verlag: Cambridge University Press

Buch, Englisch, Band 79, 310 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 509 g

Reihe: 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.

Autoren/Hrsg.

Girondo, Ernesto

González-Diez, Gabino

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

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

Über Autor(innen)

Girondo, Ernesto
Ernesto Girondo is Profesor Titular de Geometría y Topología in the Department of Mathematics at Universidad Autónoma de Madrid.

González-Diez, Gabino
Gabino González-Diez is Catedrático de Geometría y Topología in the Department of Mathematics at Universidad Autónoma de Madrid.