Large genus asymptotics of super Weil-Petersson volumes

2025/01/14 by Huang, Xuanyu
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2501.07848

Abstract

In this paper, we obtain the asymptotic expansions of super intersection numbers and prove that the associated coefficients are polynomials. Moreover, we give an algorithm which can explicitly compute these coefficients. As an application, we prove the existence of a complete asymptotic expansion of super Weil-Petersson volumes in the large genus. This generalizes the celebrated work of Mirzakhani-Zograf. We also confirm two conjectural formulae proposed by Griguolo-Papalini-Russo-Seminara.

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