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arXiv · 1912.07720

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

Bryson Owens·Seamus Somerstep
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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.

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Bryson Owens, Seamus Somerstep. 2019-12-16. Boundary Expression for Chern Classes of the Hodge Bundle on Spaces of Cyclic Covers. https://doi.org/10.2140/involve.2021.14.571

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