Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials

Résumé

We prove a closed formula for the integral of a power of a single $\psi$-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 $\psi$-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.

Dates et versions

hal-03835412 , version 1 (31-10-2022)

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Matteo Costantini, Adrien Sauvaget, Johannes Schmitt. Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials. 2022. ⟨hal-03835412⟩
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