A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle
Algebraic Geometry
2009-07-28 v3 Algebraic Topology
Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0810.2488,
title = {A representation-valued relative Riemann-Hurwitz theorem and the Hurwitz-Hodge bundle},
author = {Tyler J. Jarvis and Takashi Kimura},
journal= {arXiv preprint arXiv:0810.2488},
year = {2009}
}
Comments
Some errors corrected, and additional details provided. Moved several examples and applications to a subsequent paper