Virasoro constraints and descendant Hurwitz-Hodge Integrals

TL;DR

This paper applies Virasoro constraints to the Gromov-Witten theory of weighted projective stacks to derive formulas for descendant cyclic Hurwitz-Hodge integrals across higher genera.

Contribution

It introduces a novel application of Virasoro constraints to compute descendant Hurwitz-Hodge integrals in the context of weighted projective stacks.

Findings

Derived explicit formulas for higher genus descendant cyclic Hurwitz-Hodge integrals.

Extended Virasoro constraints to the Gromov-Witten theory of weighted projective stacks.

Provided new computational tools for enumerative geometry in orbifold settings.

Abstract

Virasoro constraints are applied to degree zero Gromov-Witten theory of weighted projective stacks $\mathbb{P}(1,N)$ and $\mathbb{P}(1,1,N)$ to obtain formulas of descendant cyclic Hurwitz-Hodge integrals in higher genera.