Moduli spaces of quadratic differentials |
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Authors: | William A Veech |
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Institution: | (1) Department of Mathematics, Rice University, 77251 Houston, TX, USA |
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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.
Research supported by NSF-MCS-8219148 and NSF-DMS-8521620. |
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