Volumes and Siegel–Veech constants of H(2G − 2) and Hodge integrals
Abstract
In the 80's H. Masur and W. Veech defined two numerical in-variants of strata of abelian differentials: the volume and the Siegel-Veech constant. Based on numerical experiments, A. Eskin and A. Zorich proposed a series of conjectures for the large genus asymptotics of these invariants. By a careful analysis of the asymptotic behavior of quasi-modular forms, D. Chen, M. Moeller, and D. Zagier proved that this conjecture holds for strata of differentials with simple zeros. Here, with a mild assumption of existence of a good metric, we show that the conjecture holds for the other extreme case, i.e. for strata of differentials with a unique zero. Our main ingredient is the expression of the numerical invariants of these strata in terms of Hodge integrals on moduli spaces of curves.
Keywords
Moduli space of curves
Translation surfaces
Masur–Veech volumes
Hodge integrals
Mathematics Subject Classification. 14H15 14N10 30F30 30F60 14C17 Moduli space of curves translation surfaces Masur-Veech volumes Hodge integrals
Mathematics Subject Classification. 14H15
14N10
30F30
30F60
14C17 Moduli space of curves
translation surfaces
Masur-Veech volumes
Origin | Files produced by the author(s) |
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