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Towards large genus asymptotics of intersection numbers on moduli spaces of curves

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Abstract

We explicitly compute the diverging factor in the large genus asymptotics of the Weil–Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicative constant we prove the existence of a complete asymptotic expansion of the Weil–Petersson volumes in the inverse powers of the genus with coefficients that are polynomials in n. This is done by analyzing various recursions for the more general intersection numbers of tautological classes, whose large genus asymptotic behavior is also extensively studied.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Maryam Mirzakhani

  2. St. Petersburg Department, Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia

    Peter Zograf

  3. Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O. 29B, St. Petersburg, 199178, Russia

    Peter Zograf

Authors
  1. Maryam Mirzakhani
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  2. Peter Zograf
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Corresponding author

Correspondence to Peter Zograf.

Additional information

The work of MM was partially supported by NSF and Simons grants. The work of PZ was supported by the Government of the Russian Federation megagrant 11.G34.31.0026, by JSC “Gazprom Neft”, and by the RFBR grant 14-01-00373-A. PZ also gratefully acknowledges the hospitality and support of MPIM (Bonn), QGM (Aarhus) and SCGP (Stony Brook).

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Mirzakhani, M., Zograf, P. Towards large genus asymptotics of intersection numbers on moduli spaces of curves. Geom. Funct. Anal. 25, 1258–1289 (2015). https://doi.org/10.1007/s00039-015-0336-5

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  • DOI: https://doi.org/10.1007/s00039-015-0336-5

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