Spectral Covers
Abstract
This is a survey of various results about spectral covers and their relationship to Higgs bundles. To a G-principal Higgs bundle on a variety S corresponds a cameral cover \widetilde{S} of S (a W-Galois cover, where W is the Weyl group of G) together with a sheaf on \widetilde{S} which in simple cases is a line bundle, and is W-equivariant up to certain twists and shifts. Various other types of spectral covers, depending on the choice of a representation or weight of G, arise as associated objects of \widetilde{S}. We focus on the decomposition of the Picards of these spectral covers into Pryms (this includes various well-known Prym identities as special cases) and on the interpretation, in the spirit of Hitchin's abelianization program, of a distinguished Prym component as parameter space for higgs bundles.
Keywords
Cite
@article{arxiv.alg-geom/9505009,
title = {Spectral Covers},
author = {Ron Donagi},
journal= {arXiv preprint arXiv:alg-geom/9505009},
year = {2008}
}