Cohomology classes of strata of differentials

Sauvaget, Adrien

doi:10.2140/gt.2019.23.1085

Cited by 24 publications

(40 citation statements)

References 40 publications

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“…In Section 3 we prove the induction formula for the integrals of ξ-classes (Theorem 1.6). The main ingredient in this proof is the computation of the cohomlogy classes Poincaré-dual to [PH(µ)] ∈ H * (PH g ) as in [15] (we will recall a simplified version of this computation here). Finally, in Section 4 we analyze the asymptotic behavior of the integrals of ξ-classes to deduce Theorem 1.9.…”

Section: Intersection Numbers On Strata Of Differentialsmentioning

confidence: 99%

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Volumes and Siegel–Veech constants of $${\mathcal{H}}$$H (2G − 2) and Hodge integrals

Sauvaget

2018

Geom. Funct. Anal.

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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 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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Section: Intersection Numbers On Strata Of Differentialsmentioning

confidence: 99%

“…The main tool to prove Theorem 1.6 will be the induction formula established in [15] to compute the cohomology classes [A g (Z)] in H * (PH g,n ). We will state a simplified version of this induction formula because we only need to compute the class λ g α 0 g (Z) ∈ H * (M g,n ).…”

Section: Stable Differentialsmentioning

confidence: 99%

Volumes and Siegel–Veech constants of $${\mathcal{H}}$$H (2G − 2) and Hodge integrals

Sauvaget

2018

Geom. Funct. Anal.

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“…Expression (14) for c (1) cyl (H(m)) and bound (15) for ε cyl (m) imply existence of a universal constant B such that the ratio c (1) cyl (H(m)) dim C H(m) − 1 can be represented in the form (16) with ε area (m) satisfying bound (17).…”

Section: 2mentioning

confidence: 99%

“…Second, the work of Sauvaget [18] established (1.1) in the case of the minimal stratum m = (2g − 2), when ω has one zero with multiplicity 2g − 2. Through an analysis of Hodge integrals on the moduli space of curves (based on his earlier work [17]), he shows as Theorem 1.9 of [18] that…”

Section: Introductionmentioning

confidence: 99%

Large genus asymptotics for volumes of strata of abelian differentials

Aggarwal

2020

J. Amer. Math. Soc.

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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 volumeThis confirms a prediction of Eskin-Zorich and generalizes some of the recent results of Chen-Möller-Zagier and Sauvaget, who established these limiting statements in the special cases m = 1 2g−2 and m = (2g − 2), respectively.We also include an Appendix by Anton Zorich that uses our main result to deduce the large genus asymptotics for Siegel-Veech constants that count certain types of saddle connections.

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“…Second, the work of Sauvaget [17] established (1.3) in the case when m = (2g − 2); this corresponds to the "opposite" stratum in which ω has one zero with multiplicity 2g − 2. Through an analysis of Hodge integrals on the moduli space of curves (based on his earlier work [18]…”

Section: Large Genus Asymptoticsmentioning

confidence: 99%

Large Genus Asymptotics for Siegel–Veech Constants

Aggarwal

2019

Geom. Funct. Anal.

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In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum H(α) of Abelian differentials. The first is the saddle connection Siegel-Veech constant c m i ,m j sc H(α) counting saddle connections between two distinct, fixed zeros of prescribed orders m i and m j , and the second is the area Siegel-Veech constant carea H(α) counting maximal cylinders weighted by area. By combining a combinatorial analysis of explicit formulas of Eskin-Masur-Zorich that express these constants in terms of Masur-Veech strata volumes, with a recent result for the large genus asymptotics of these volumes, we show that c m i ,m j sc H(α) = (m i + 1)(m j + 1) 1 + o(1) and carea H(α) = 1 2 + o(1), both as |α| = 2g − 2 tends to ∞. The former result confirms a prediction of Zorich and the latter confirms one of Eskin-Zorich in the case of connected strata.

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Cohomology classes of strata of differentials

Cited by 24 publications

References 40 publications

Volumes and Siegel–Veech constants of $${\mathcal{H}}$$H (2G − 2) and Hodge integrals

Volumes and Siegel–Veech constants of $${\mathcal{H}}$$H (2G − 2) and Hodge integrals

Large genus asymptotics for volumes of strata of abelian differentials

Large Genus Asymptotics for Siegel–Veech Constants

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