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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Degenerations of quadratic differentials on $\mathbb{CP}^1$

Corentin Boissy

Geometry & Topology 12 (2008) 1345–1386
Abstract

We describe the connected components of the complement of a natural “diagonal” of real codimension 1 in a stratum of quadratic differentials on 1. 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.

Keywords
quadratic differentials, saddle connections, Siegel–Veech constants
Mathematical Subject Classification 2000
Primary: 32G15
Secondary: 30F30, 57R30
References
Publication
Received: 9 September 2007
Accepted: 16 January 2008
Published: 4 June 2008
Proposed: Benson Farb
Seconded: Walter Neumann, Jean-Pierre Otal
Authors
Corentin Boissy
IRMAR
Université Rennes 1
Campus de Beaulieu
35042 Rennes cedex
France
http://perso.univ-rennes1.fr/corentin.boissy