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.
Cite this article
Erwan Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities. Comment. Math. Helv. 79 (2004), no. 3, pp. 471–501DOI 10.1007/S00014-004-0806-0