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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