All the $\lambda_1$'s on cyclic admissible covers

TL;DR

This paper computes the degrees of Hurwitz-Hodge classes and the first Chern class of the Hodge bundle on moduli spaces of cyclic admissible covers, providing explicit formulas and relations in algebraic geometry.

Contribution

It provides explicit calculations of Hurwitz-Hodge class degrees and expresses the divisor class in higher dimensions as a combination of known classes.

Findings

Degree of Hurwitz-Hodge classes on one-dimensional moduli spaces computed

First Chern class of the Hodge bundle calculated for all one-dimensional moduli spaces

Divisor class expressed as a linear combination of psi classes and boundary strata in higher dimensions

Abstract

We compute the degree of Hurwitz-Hodge classes $\lambda_1^e$ on one dimensional moduli spaces of cyclic admissible covers of the projective line. We also compute the degree of the the first Chern class of the Hodge bundle $\lambda_1$ for all one dimensional moduli spaces. In higher dimension, we express the divisor class $\lambda_1$ as a linear combination of $\psi$ classes and boundary strata.