Abelian Hurwitz-Hodge integrals

Details Abelian Hurwitz-Hodge integrals Abelian Hurwitz-Hodge integrals

2008-03-04

arxiv.org/abs/0803.0499v2

Mathematics

Algebraic Geometry

25 pages, revised version. Calculation of 1-point Hurwitz-Hodge series added

Scientific paper

Hodge classes on the moduli space of admissible covers with monodromy group G are associated to irreducible representations of G. We evaluate all linear Hodge integrals over moduli spaces of admissible covers with abelian monodromy in terms of multiplication in an associated wreath group algebra. In case G is cyclic and the representation is faithful, the evaluation is in terms of double Hurwitz numbers. In case G is trivial, the formula specializes to the well-known result of Ekedahl-Lando-Shapiro-Vainshtein for linear Hodge integrals over the moduli space of curves in terms of single Hurwitz numbers.

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