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 μ3-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 λ1. We also consider covers with a μ2-action for which we compute λ2 as a linear combination of codimension-2 boundary strata.

Keywords
admissible covers, Hodge bundle, tautological classes, moduli space of curves
Mathematical Subject Classification 2010
Primary: 14H10
Milestones
Received: 16 December 2019
Revised: 1 March 2021
Accepted: 28 April 2021
Published: 23 October 2021

Communicated by Michael Jablonski
Authors
Bryson Owens
Department of Mathematics
Colorado State University
Fort Collins, CO
United States
Seamus Somerstep
Department of Mathematics
Colorado State University
Fort Collins, CO
United States
Renzo Cavalieri
Department of Mathematics
Colorado State University
Fort Collins, CO
United States