Degenerations of quadratic differentials on ℂℙ1

Boissy, Corentin

doi:10.2140/gt.2008.12.1345

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Degenerations of quadratic differentials on $\mathbb{CP}^1$

Corentin Boissy

Geometry & Topology 12 (2008) 1345–1386

DOI: 10.2140/gt.2008.12.1345

Abstract

We describe the connected components of the complement of a natural “diagonal” of real codimension $1$ in a stratum of quadratic differentials on ${ℂ ℙ}^{1}$ . 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

Volume 12, issue 3 (2008)