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

Erwan Lanneau (1, 2, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Abelian differentials; quadratic differentials; moduli spaces; hyperelliptic surfaces

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Erwan Lanneau. Hyperelliptic Components of the Moduli Spaces of Quadratic Differentials with Prescribed Singularities. Commentarii Mathematici Helvetici, 2004, 79, pp.471-501. ⟨hal-00013159⟩