Masur-Veech volumes and intersection theory on moduli spaces of Abelian 
differentials

Chen, Dawei; Möller, Martin; Sauvaget, Adrien; Zagier, Don

doi:10.1007/s00222-020-00969-4

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Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials

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Chen, Dawei
Max Planck Institute for Mathematics, Max Planck Society;

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Möller, Martin
Max Planck Institute for Mathematics, Max Planck Society;

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Sauvaget, Adrien
Max Planck Institute for Mathematics, Max Planck Society;

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Zagier, Don
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00222-020-00969-4
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Chen-Möller-Sauvaget-Zagier_Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials_2020.pdf
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Citation

Chen, D., Möller, M., Sauvaget, A., & Zagier, D. (2020). Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials. Inventiones Mathematicae, 222(1), 283-373. doi:10.1007/s00222-020-00969-4.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9B2B-C

Abstract

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, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata.
We also show that the same results hold for the spin and hyper-elliptic components of the strata.