Journal d’Analyse Mathematique

, Volume 55, Issue 1, pp 117–171

Moduli spaces of quadratic differentials

  • William A. Veech

DOI: 10.1007/BF02789200

Cite this article as:
Veech, W.A. J. Anal. Math. (1990) 55: 117. doi:10.1007/BF02789200


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 Lpπ), 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.

Copyright information

© Hebrew University of Jerusalem 1990

Authors and Affiliations

  • William A. Veech
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA