A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle

Details A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle

2008-10-14

arxiv.org/abs/0810.2488v3

Mathematics

Algebraic Geometry

Some errors corrected, and additional details provided. Moved several examples and applications to a subsequent paper

Scientific paper

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible G-covers. This formula can be interpreted as a representation-ring-valued relative Riemann-Hurwitz formula for families of admissible G-covers.

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