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RECURSION FOR MASUR-VEECH VOLUMES OF MODULI SPACES OF QUADRATIC DIFFERENTIALS

Part of: Curves Deformations of analytic structures

Published online by Cambridge University Press:  08 January 2021

Maxim Kazarian Open the ORCID record for Maxim Kazarian [Opens in a new window]
Maxim Kazarian*
Affiliation:
National Research University Higher School of Economics, Skolkovo Institute of Science and Technology, ([email protected])
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Abstract

We derive a quadratic recursion relation for the linear Hodge integrals of the form $\langle \tau _{2}^{n}\lambda _{k}\rangle $ . These numbers are used in a formula for Masur-Veech volumes of moduli spaces of quadratic differentials discovered by Chen, Möller and Sauvaget. Therefore, our recursion provides an efficient way of computing these volumes.

Keywords

Masur-Veech volumesHodge integralsKP hierarchy

MSC classification

Primary: 14H10: Families, moduli (algebraic)
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 4 , July 2022 , pp. 1471 - 1476
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

A. Aggarwal, Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials, arXiv:2004.05042.Google Scholar
Aggarwal, A., Delecroix, V., Goujard, E., Zograf, P. and Zorich, A., Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials. arXiv:1912.11702.Google Scholar
Athreya, J. S., Eskin, A. and Zorich, A., Right-angled billiards and volumes of moduli spaces of quadratic differentials on CP1, Ann. Sci. Ec. Norm. Super. (4) 49(6) (2016), 1311–1386 (with an appendix by Jon Chaika).CrossRefGoogle Scholar
Buryak, A., ILW equation for the Hodge integrals revisited, Math. Res. Lett. 23(3) (2016), 675–683. arXiv:1505.05911.CrossRefGoogle Scholar
Chen, D., Möller, M. and Sauvaget, A., Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials. arXiv:1912.02267 (with an appendix by G. Borot, A. Giacchetto and D. Lewanski).Google Scholar
Delecroix, V., Goujard, E., Zograf, P. and Zorich, A., Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves. arXiv:1908.08611.Google Scholar
Itzykson, C. and Zuber, J.-B., Combinatorics of the modular group. II. The Kontsevich integrals, Int. J. Mod. Phys. A 7 (1992), no. 23, 5661–5705.CrossRefGoogle Scholar
Kazarian, M., KP hierarchy for Hodge integrals, Adv. Math. 221(1) (2009), 1–21. arXiv:0809.3263.CrossRefGoogle Scholar
Kontsevich, M., Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147(1) (1992), 1–23.CrossRefGoogle Scholar
Manin, Y. I. and Zograf, P., Invertible cohomological field theories and Weil-Petersson volumes, Ann. Inst. Fourier (Grenoble) 50(2) (2000), 519–535.CrossRefGoogle Scholar
Witten, E., Two-dimensional gravity and intersection theory on moduli space, in Surveys in Differential Geometry, pp. 243–310 (Lehigh University, Bethlehem, PA, 1991).Google Scholar
Yang, D., Zagier, D. and Zhang, Y., Masur-Veech volumes of quadratic differentials and their asymptotics. arXiv:2005.02275.Google Scholar
Zvonkine, D., Enumeration of ramified coverings of the sphere and $2$ -dimensional gravity. arXiv:math/0506248.Google Scholar