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

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

2002-10-07

arxiv.org/abs/math/0210099v2

Commentarii Mathematici Helvetici 79 no. 3, (2004) 471--501

Mathematics

Geometric Topology

references added. 23 pages, 5 figures

Scientific paper

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.

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