An Infinitesimal Study of the Moduli of Hitchin Pairs

Biswas, Indranil; Ramanan, S.

doi:10.1112/jlms/49.2.219

Cited by 133 publications

(166 citation statements)

References 8 publications

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“…We also should mention the paper [6] by Biswas and Ramanan. They study the infinitesimal deformation space of principal Higgs bundles on a curve using hypercohomology.…”

Section: Introductionmentioning

confidence: 94%

Homological Algebra of Twisted Quiver Bundles

Gothen¹,

King²

2005

J. London Math. Soc.

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Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed space. We show that the category of such representations is an abelian category with enough injectives by constructing an explicit injective resolution. Using this explicit resolution, we find a long exact sequence that computes the Ext groups in this new category in terms of the Ext groups in the old category. The quiver formulation is directly reflected in the form of the long exact sequence. We also show that under suitable circumstances, the Ext groups are isomorphic to certain hypercohomology groups.

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“…We also should mention the paper [6] by Biswas and Ramanan. They study the infinitesimal deformation space of principal Higgs bundles on a curve using hypercohomology.…”

Section: Introductionmentioning

confidence: 94%

Homological Algebra of Twisted Quiver Bundles

Gothen¹,

King²

2005

J. London Math. Soc.

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“…-Reprenons les notations de 1. 9. En particulier, on a un revêtement fini plat ρ κ × t → c qui permet de réaliser c comme le quotient invariant de ρ κ × t par W π 0 (κ).…”

Section: Le Cas Des Groupes Endoscopiques -Considérons Une Donnée Enunclassified

Le lemme fondamental pour les algèbres de Lie

2010

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“…For arbitrary (affine) reductive groups G the moduli spaces Higgs G,X are holomorphic symplectic as well, see [Hit87b], [BR94], [Sim94]. Their symplectic structure can be expressed either via the duality pairing for H 1 (C • (P,θ) ), or in Dolbeault terms, as in (3.4).…”

Section: ) Is Non-singular and Is A Translate Of The Prym Variety Prymmentioning

confidence: 99%

“…The infinitesimal deformations of a pair (P, θ) are controlled, as shown in [BR94], [Hit92], [Nit91], by H 1 (C • (P,θ) ), where C • (P,θ) is the complex…”

Section: K X -Valued G-higgs Bundles On Curvesmentioning

confidence: 99%