Teichmüller spaces, triangle groups and Grothendieck dessins

Abstract

This chapter concerns Teichmüller theory from the point of view of the deformation theory of algebraic curves. The author surveys in particular the deformation theory of Veech’s discs and other Teichmüller discs, of families associated to triangle groups and arithmetically defined curves, with a section on Grothendieck’s dessins d’enfants.