#### Vol. 14, No. 4, 2021

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Boundary expression for Chern classes of the Hodge bundle on spaces of cyclic covers

### Bryson Owens, Seamus Somerstep and Renzo Cavalieri

Vol. 14 (2021), No. 4, 571–594
##### Abstract

We compute an explicit formula for the first Chern class of the Hodge bundle over the space of admissible ${\mu }_{3}$-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 families of Hodge integrals containing ${\lambda }_{1}$. We also consider covers with a ${\mu }_{2}$-action for which we compute ${\lambda }_{2}$ as a linear combination of codimension-2 boundary strata.

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##### Keywords
admissible covers, Hodge bundle, tautological classes, moduli space of curves
Primary: 14H10