Volumes and Siegel–Veech constants of H(2G − 2) and Hodge integrals - Sorbonne Université Access content directly
Journal Articles Geometric And Functional Analysis Year : 2018

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.
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Dates and versions

hal-01972098 , version 1 (07-01-2019)
hal-01972098 , version 2 (13-05-2024)

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Adrien Sauvaget. Volumes and Siegel–Veech constants of H(2G − 2) and Hodge integrals. Geometric And Functional Analysis, 2018, 28 (6), pp.1756-1779. ⟨10.1007/s00039-018-0468-5⟩. ⟨hal-01972098v2⟩
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