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The gerbe of Higgs bundles

R. Donagi·D. Gaitsgory
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Abstract

The purpose of this work is to describe the (category of) Higgs bundles on a complex scheme X having a given cameral cover X~. We show that this category is a T_{X~}-gerbe, where T_{X~} is a certain sheaf of abelian groups on X, and we describe the class of this gerbe precisely. In particular, it follows that the set of isomorphism classes of Higgs bundles with a fixed cameral cover X~ is a torsor over the group H^1(X, T_{X~}), which itself parametrizes T_{X~}-torsors on X. This underlying group can be described as a generalized Prym variety, whose connected component is either an abelian variety or a degeneration thereof.

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R. Donagi, D. Gaitsgory. 2002-04-04. The gerbe of Higgs bundles. https://arxiv.org/abs/math/0005132

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