JournalscmhVol. 79 , No. 3DOI 10.1007/s00014-004-0806-0

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

  • Erwan Lanneau

    Institut de Mathématiques de Luminy (IML), Marseille, France
Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities cover

Abstract

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.