Hyperelliptic Components of the Moduli Spaces of Quadratic Differentials with Prescribed Singularities

Erwan Lanneau

Published 2002-10-07, updated 2005-03-07Version 2

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 genera the strata of meromorphic quadratic differentials are either connected, or have exactly two connected components, and one of the two components is hyperelliptic.