DAGA Seminar: Dessins d'Enfants and Algebraic Geometry

Tuesday 8 May 2012 - George Shabat


Thursday May 8, 2012, h.11:00, room 1BC45
George Shabat (Moscow State and Russian State University for the Humanities)
"Dessins d'Enfants and Algebraic Geometry"

A dessin d'enfant is such a graph on a compact oriented surface that its complement is homeomorphic to a disjoint union of 2-cells. It turns out (understood by Grothendieck in 1970's) that the category of dessins d'enfants, being appropriately defined, is equivalent to the category of BELYI PAIRS, i.e. the category of smooth complete curves over the field of algebraic numbers together with a covering of the projective line ramified only over a three points. Therefore the combinatorial topology of graphs on surfaces is somewhat equivalent to a part of arithmetic geometry; the precise statements will be given in the first part of the talk and some examples will be presented. In the second part the deeper relations of the dessins d'enfants theory with algebraic geometry will be discussed, mainly related to the Penner-Kontzevich dessins-labelled stratification of moduli spaces of curves with marked points.

Rif. int. A. Bertapelle

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