Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech

Translated title of the contribution: Contribution of one-cylinder square-tiled surfaces to masur-veech volumes

Vincent Delecroix, Élise Goujard, Peter Zograf, Anton Zorich, Philip Engel

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting count is particularly simple and efficient in the large genus asymptotics. Using the recent results of Aggarwal and of Chen-Möller-Zagier on the long-standing conjecture about the large genus asymptotics of Masur-Veech volumes, we derive that the relative contribution is asymptotically of the order 1/d, where d is the dimension of the stratum. Similarly, we evaluate the contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes of low-dimensional strata in the moduli space of quadratic differentials. We combine this count with our recent result on equidistribution of one-cylinder square-tiled surfaces translated to the language of interval exchange transformations to compute empirically approximate values of the Masur-Veech volumes of strata of quadratic differentials of all small dimensions.

Translated title of the contributionContribution of one-cylinder square-tiled surfaces to masur-veech volumes
Original languageFrench
Pages (from-to)223-274
Number of pages52
JournalAsterisque
Volume415
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Masur-Veech volume
  • Moduli space of Abelian differentials
  • Rauzy diagram
  • Separatrix diagram
  • Square-tiled surface

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