# 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…
Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials
In this paper we analyze the large genus asymptotics for intersection numbers between $\psi$-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a
Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• Mathematics
• 2019
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of
Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes
• Mathematics
• 2019
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
Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• Mathematics
Inventiones mathematicae
• 2022
We study the combinatorial geometry of a random closed multicurve on a surface of large genus and of a random square-tiled surface of large genus. We prove that primitive components of a random
The Large Genus Asymptotic Expansion of Masur–Veech Volumes
• A. Sauvaget
• Mathematics
International Mathematics Research Notices
• 2019
We study the asymptotic behavior of Masur–Veech volumes as the genus goes to infinity. We show the existence of a complete asymptotic expansion of these volumes that depends only on the genus and
Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials
• Mathematics
• 2019
We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros. As applications,
Uniform Lower Bound for Intersection Numbers of ψ-Classes
• Mathematics
• 2020
We approximate intersection numbers $\langle \psi_1^{d_1} \dots \psi_n^{d_n}\rangle_{g,n}$ on Deligne--Mumford's moduli space $\overline{\mathcal{M}}_{g,n}$ of genus $g$ stable complex curves with
Conjectural Large Genus Asymptotics of Masur–Veech Volumes and of Area Siegel–Veech Constants of Strata of Quadratic Differentials
• Mathematics
• 2019
We state conjectures on the asymptotic behavior of the Masur–Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel–Veech
Billiards in right triangles and orbit closures in genus zero strata
We classify GL(2,R) orbit closures of rank at least two in hyperelliptic components of strata of Abelian and quadratic differentials. As a consequence, the orbit closure of the unfolding of every

## References

SHOWING 1-10 OF 28 REFERENCES
Large Genus Asymptotics for Siegel–Veech Constants
• A. Aggarwal
• Mathematics
Geometric and Functional Analysis
• 2019
In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum $\mathcal{H} (\alpha)$ of Abelian differentials. The
Volumes and Siegel–Veech constants of $${\mathcal{H}}$$H (2G − 2) and Hodge integrals
• A. Sauvaget
• Mathematics
Geometric and Functional Analysis
• 2018
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
Topological recursion for Masur-Veech volumes.
• Mathematics
• 2019
We study the Masur--Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes
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
• Mathematics
• 2016
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
• Mathematics
• 2019
We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of
Moduli spaces of Abelian differentials: The principal boundary, counting problems, and the Siegel–Veech constants
• Mathematics
• 2002
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
• Mathematics
• 2019
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
On the large genus asymptotics of Weil-Petersson volumes
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
Towards large genus asymptotics of intersection numbers on moduli spaces of curves
• Mathematics
• 2011
We explicitly compute the diverging factor in the large genus asymptotics of the Weil–Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicative