Boundary Expression for Chern Classes of the Hodge Bundle on Spaces of Cyclic Covers

Abstract

We compute an explicit formula for the first Chern class of the Hodge Bundle over the space of admissible cyclic $\mathbb{Z}/3\mathbb{Z}$ covers of $n$-pointed rational stable curves as a linear combination of boundary strata. We then apply this formula to give a recursive formula for calculating certain Hodge integrals containing ${\lambda }_1$. We also consider covers with a $\mathbb{Z}/2\mathbb{Z}$ action for which we compute ${\lambda }_2$ as a linear combination of codimension two boundary strata.

References in corpus (1)

• A hyperelliptic Hodge integral

Cited by in corpus (1)

• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves