Large genus asymptotics for volumes of strata of abelian differentials

@article{Aggarwal2020LargeGA,
  title={Large genus asymptotics for volumes of strata of abelian differentials},
  author={Amol Aggarwal},
  journal={Journal of the American Mathematical Society},
  year={2020}
}
  • A. Aggarwal
  • Published 15 April 2018
  • Mathematics
  • Journal of the American Mathematical Society
<p>In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by Eskin-Okounkov to exactly evaluate these quantities, we show that the volume <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="nu 1 left-parenthesis script upper H 1 left-parenthesis m right-parenthesis right-parenthesis"> <mml:semantics… 
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    International Mathematics Research Notices
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References

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  • Mathematics
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In the 80’s H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel–Veech constant. Based on numerical experiments, A. Eskin and A. Zorich…
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VOLUMES AND SIEGEL-VEECH CONSTANTS OF H(2g − 2) AND HODGE INTEGRALS
In the 80’s H. Masur and W. Veech defined two numerical invariants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich…
Quasimodularity and large genus limits of Siegel-Veech constants
Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms.…
Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
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Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel–Veech constants
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment…
Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes
We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting…
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A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of…
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