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

2011/12/06 by Maryam Mirzakhani, Mirzakhani, Maryam, Peter Zograf +1 · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1112.1151

openalex publication_date 2011/12/06 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Citations

• Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

Cited by

• Local Weyl law and length-minimising loops on hyperbolic surfaces
• Counting AdS Vacua
• A natural basis for intersection numbers
• Asymptotics of shortest filling closed multi-geodesics

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