Commentarii Mathematici Helvetici


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Volume 79, Issue 3, 2004, pp. 471–501
DOI: 10.1007/s00014-004-0806-0

Published online: 2004-09-30

Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities

Erwan Lanneau[1]

(1) Institut de Mathématiques de Luminy (IML), Marseille, France

Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up to the four exceptional cases in low dimensional stratum, any stratum of meromorphic quadratic differentials is either connected, or has exactly two connected components. In this last case, one component is hyperelliptic, the other not.

Keywords: quadratic differentials, moduli space, measured foliationsm, Teichmüller geodesic flow

Lanneau Erwan: Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities. Comment. Math. Helv. 79 (2004), 471-501. doi: 10.1007/s00014-004-0806-0