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

Owens, Bryson; Somerstep, Seamus; Cavalieri, Renzo

doi:10.2140/involve.2021.14.571

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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

DOI: 10.2140/involve.2021.14.571

Abstract

We compute an explicit formula for the first Chern class of the Hodge bundle over the space of admissible $μ_{3}$ -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 $λ_{1}$ . We also consider covers with a $μ_{2}$ -action for which we compute $λ_{2}$ 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

Vol. 14, No. 4, 2021