The gerbe of Higgs bundles

Details The gerbe of Higgs bundles The gerbe of Higgs bundles

2000-05-13

arxiv.org/abs/math/0005132v3

Transform. Groups 7 (2002) 109-153

Mathematics

Algebraic Geometry

47 pages; two added sections contain applications to Higgs bundles with values and to bundles on elliptic fibrations

Scientific paper

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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