Integrals of ψ-classes on twisted double ramification cycles and spaces of differentials

2021/12/08 by Matteo Costantini, Costantini, Matteo, Adrien Sauvaget +3 · 2 citations
Mathematics · Physics and Astronomy · #14C17 #14H10 #30F30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2112.04238

openalex publication_date 2021/12/08 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28

Abstract

We prove a closed formula for the integral of a power of a single ψ-class on strata of k-differentials. In many cases, these integrals correspond to intersection numbers on twisted double ramification cycles. Then we conjecture an expression of a refinement of double ramification cycles according to the parity of spin structures. Assuming that this conjecture is valid, we also compute the integral of a single ψ-class on the even and odd components of strata of k-differentials. As an application of these results we give a closed formula for the Euler characteristic of components of minimal strata of abelian differentials.

Cited by

• Virtual volumes of strata of meromorphic differentials with simple poles
• Meromorphic differentials and twisted DR hierarchies for the Hodge CohFT

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