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Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech. / Delecroix, Vincent; Goujard, Élise; Zograf, Peter; Zorich, Anton; Engel, Philip.

In: Asterisque, Vol. 415, 2020, p. 223-274.

Research output: Contribution to journal › Article › peer-review

Harvard

Delecroix, V, Goujard, É, Zograf, P, Zorich, A & Engel, P 2020, 'Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech', Asterisque, vol. 415, pp. 223-274. https://doi.org/10.24033/AST.1107

APA

Delecroix, V., Goujard, É., Zograf, P., Zorich, A., & Engel, P. (2020). Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech. Asterisque, 415, 223-274. https://doi.org/10.24033/AST.1107

Vancouver

Delecroix V, Goujard É, Zograf P, Zorich A, Engel P. Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech. Asterisque. 2020;415:223-274. https://doi.org/10.24033/AST.1107

Author

Delecroix, Vincent ; Goujard, Élise ; Zograf, Peter ; Zorich, Anton ; Engel, Philip. / Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech. In: Asterisque. 2020 ; Vol. 415. pp. 223-274.

BibTeX

@article{e4a093ad140e497a9b4232c69ee30965,
title = "Contribution des surfaces {\`a} petits carreaux {\`a} un cylindre aux volumes de masur-veech",
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-M{\"o}ller-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.",
keywords = "Masur-Veech volume, Moduli space of Abelian differentials, Rauzy diagram, Separatrix diagram, Square-tiled surface",
author = "Vincent Delecroix and {\'E}lise Goujard and Peter Zograf and Anton Zorich and Philip Engel",
note = "Funding Information: Research of the second author is partially supported by a public grant as part of the FMJH. Research of Section 3 is supported by the RScF grant 16-11-10039. Research of Appendix B is partially supported by NSF grant DMS-1502585. Publisher Copyright: {\textcopyright} Ast{\'e}risque 415, SMF 2020",
year = "2020",
doi = "10.24033/AST.1107",
language = "французский",
volume = "415",
pages = "223--274",
journal = "Asterisque",
issn = "0303-1179",
publisher = "Societe Mathematique de France",

}

RIS

TY - JOUR

T1 - Contribution des surfaces à petits carreaux à un cylindre aux volumes de masur-veech

AU - Delecroix, Vincent

AU - Goujard, Élise

AU - Zograf, Peter

AU - Zorich, Anton

AU - Engel, Philip

N1 - Funding Information: Research of the second author is partially supported by a public grant as part of the FMJH. Research of Section 3 is supported by the RScF grant 16-11-10039. Research of Appendix B is partially supported by NSF grant DMS-1502585. Publisher Copyright: © Astérisque 415, SMF 2020

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Masur-Veech volume

KW - Moduli space of Abelian differentials

KW - Rauzy diagram

KW - Separatrix diagram

KW - Square-tiled surface

UR - http://www.scopus.com/inward/record.url?scp=85092210311&partnerID=8YFLogxK

U2 - 10.24033/AST.1107

DO - 10.24033/AST.1107

M3 - статья

AN - SCOPUS:85092210311

VL - 415

SP - 223

EP - 274

JO - Asterisque

JF - Asterisque

SN - 0303-1179

ER -

ID: 98426064