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Intersections of loci of admissible covers with tautological classes. (English) Zbl 1461.14037

The moduli space of admissible \(G\)-covers admits a source morphism \(\phi\) and a target morphism \(\delta\) to the respective moduli spaces of curves. In this paper the authors study the behavior of tautological classes under pullback and pushforward maps associated to \(\phi\) and \(\delta\). In particular, they obtain a combinatorial formula for the cycle class of the locus of admissible \(G\)-covers restricted to the boundary strata of the source moduli space. Morover, they show that \(\delta_{*}\phi^{*}\) sends tautological classes to tautological classes and give an explicit combinatorial description of this map. As applications, they compute the cycle classes of the hyperelliptic loci in genus five and six as well as the cycle class of the bielliptic locus in genus four.

MSC:

14H10 Families, moduli of curves (algebraic)
14H30 Coverings of curves, fundamental group
14C25 Algebraic cycles

Software:

admcycles; SageMath
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Full Text: DOI arXiv

References:

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