Open Access
2008 Degenerations of quadratic differentials on $\mathbb{CP}^1$
Corentin Boissy
Geom. Topol. 12(3): 1345-1386 (2008). DOI: 10.2140/gt.2008.12.1345


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.


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Corentin Boissy. "Degenerations of quadratic differentials on $\mathbb{CP}^1$." Geom. Topol. 12 (3) 1345 - 1386, 2008.


Received: 9 September 2007; Accepted: 16 January 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.30020
MathSciNet: MR2421130
Digital Object Identifier: 10.2140/gt.2008.12.1345

Primary: 32G15
Secondary: 30F30 , 57R30

Keywords: quadratic differentials , saddle connections , Siegel–Veech constants

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.12 • No. 3 • 2008
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