All the ${\lambda }_1$'s on cyclic admissible covers

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.