Hyperelliptic Components of the Moduli Spaces of Quadratic Differentials   with Prescribed Singularities
  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. 
Erwan Lanneau