Large-genus asymptotics conjecture for Masur–Veech volumes

Let Qg,0\mathcal{Q}_{g,0} denote the moduli space of holomorphic quadratic differentials in genus gg without marked points. Large-genus asymptotics conjecture. As g+g\to+\infty, its Masur–Veech volume satisfies

VolQg,0=4π(83)4g4(1+O(1g)).\operatorname{Vol} \mathcal{Q}_{g,0}=\frac{4}{\pi}\left(\frac{8}{3}\right)^{4g-4}\left(1+O\left(\frac{1}{g}\right)\right).

The paper records this asymptotic as conjectural, while noting that a stronger form was subsequently proved by A. Aggarwal; the exact status of this displayed form should be checked against that result.

Sources & referencesView supporting material

Primary source

Vincent Delecroix, Elise Goujard, Peter Zograf and Anton Zorich, “Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves”, arXiv:2011.05306 (2020).

Additional references

6 papers in this index state this conjecture (2004–2020). The statement above is taken from the most recent of them; the others are arXiv:1912.02267, arXiv:1908.08611, arXiv:1101.4792, arXiv:0812.0544, arXiv:math/0401013.

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