The Gerbe Of Higgs Bundles
By R. Donagi, D. Gaitsgory. 2000
116 citations recorded by the source corpus.
1(X, T \bar{X}) which itself parametrizes T \bar{X} torsors on X. This underlying group H1(X, T \bar{X}) can be described as a generalized Prym variety, whose connected component is either an abelian variety or a degenerate abelian variety. The main part of the work deals with abstract Higgs bundles; in the last two sections we derive the applications to Higgs bundles valued in a line bundle K and to bundles on elliptic fibrations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1335984dcd660d74f57e4e8d51e0c75ba9fbce0a
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Geometric representations of graded and rational Cherednik algebras (2014, methodology): “The alternative construction of the regular centralizers given in [10] then shows that each Jã is canonically isomorphic to the same group scheme J̃ over Spec OFm such that it is a subgroup scheme of T ⊗OFm with the same generic fiber.”
- Global topology of the Hitchin system (2011, methodology): “Here we sketch a quick definition of gerbes for more details see [49],[88] and [25].”
- Electric-Magnetic Duality And The Geometric Langlands Program (2006, background): “The geometry underlying this T -duality was investigated in [22] and subsequently in [23] for any semi-simple Lie group G.”
- Equivariant homology and K-theory of affine Grassmannians and Toda lattices (2005, background): “) The following Proposition is a generalization of [5] 11.”
- Semistable modules over Lie algebroids in positive characteristic (2013, background): “ith it set-theoretically. Note that in the curve case there exists a different interpretation of Higgs bundles using cameral covers. Such an approach allows to deal with general reductive groups (see [DG] for the characteristic zero case). In positive characteristic the analogous construction requir”
- Mirror symmetry, Langlands duality, and the Hitchin system (2002, background): “The category of T -torsors constitutes a sheaf of Picard categories (or stack) over M . Sheaf of categories here means roughly what one would expect, but the precise definition is somewhat technical; a convenient reference is Donagi-Gaitsgory [ 14 ].”
- Autoduality of compactified Jacobians for curves with plane singularities (2010, background): “The morphism FlagS → Hilb ′ S is a cameral cover for the group GL(n) in the sense of [10].”
- Langlands duality for Hitchin systems (2006, methodology): “The gerbe Higgs of G-Higgs bundles was introduced and analyzed in [DG02].”
- Spectral Networks (2012, unknown): “[55] where it was introduced, and [50] for a very precise description of the abelianization map in the more general setting of an arbitrary Lie group G.”