Degenerations of quadratic differentials on CP1

Corentin Boissy (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We describe the connected components of the complement of a natural "diagonal" of real codimension 1 in a stratum of quadratic differentials on CP1. We establish a natural bijection between the set of these connected components and the set of generic configurations that appear on such "flat spheres". We also prove that the stratum has only one topological end. Finally, we elaborate a necessary toolkit destined to evaluation of the Siegel-Veech constants.

Mots clés: Quadratic differentials; configurations; saddle connections; Siegel-Veech constants

Domaines: Topologie géométrique [math.GT]

Corentin Boissy. Degenerations of quadratic differentials on CP1. Geometry and Topology, 2008, 12, pp.1345-1386. ⟨hal-00168265⟩