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Moduli spaces of quadratic differentials

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Abstract

The cotangent bundle ofJ (g, n) is a union of complex analytic subvarieties, V(π), the level sets of the function “singularity pattern” of quadratic differentials. Each V(π) is endowed with a natural affine complex structure and volume element. The latter contracts to a real analytic volume element, Μπ, on the unit hypersurface, V1(π), for the Teichmüller metric. Μπ is invariant under the pure mapping class group, γ(g, n), and a certain class of functions is proved to be Lp(Μπ), 0 <p < 1, over the moduli space V1(π)/γ (g, n). In particular, Μπ(V1(π)/γ(g, n)) < ∞, a statement which generalizes a theorem by H. Masur.

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Authors and Affiliations

  1. Department of Mathematics, Rice University, 77251, Houston, TX, USA

    William A. Veech

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  1. William A. Veech
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Research supported by NSF-MCS-8219148 and NSF-DMS-8521620.

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Veech, W.A. Moduli spaces of quadratic differentials. J. Anal. Math. 55, 117–171 (1990). https://doi.org/10.1007/BF02789200

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  • DOI: https://doi.org/10.1007/BF02789200

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