All the 𝜆₁’s on cyclic admissible covers

Cavalieri, Renzo; Owens, Bryson; Somerstep, Seamus

doi:10.1090/proc/17106

All the $\lambda _1$’s on cyclic admissible covers
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by Renzo Cavalieri, Bryson Owens and Seamus Somerstep;

Proc. Amer. Math. Soc. 153 (2025), 2299-2321

DOI: https://doi.org/10.1090/proc/17106

Published electronically: March 25, 2025

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Abstract:

We compute the degrees of the first Chern class of the Hodge bundle $\lambda _1$ and of Hurwitz-Hodge classes $\lambda _1^e$ on one-dimensional moduli spaces of cyclic admissible covers of a rational curve. In higher dimension, we express the divisor class $\lambda _1$ as a linear combination of $\psi$ classes and boundary strata; we detail a computational scheme, and show some infinite family of examples for the classes $\lambda _1^e$.

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All the $\lambda _1$’s on cyclic admissible covers
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Abstract: