Equivariant Vector Bundles on Certain Affine G-Varieties

Asok, Aravind

doi:10.4310/pamq.2006.v2.n4.a7

Cited by 3 publications

(5 citation statements)

References 9 publications

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“…However the integrality of m F E is not a complete obstruction for existence of very stable bundles as examples in Remark 5. 13 for type (1,3) in rank 4 show.…”

Section: For Generic a ∈ A The Intersection W +mentioning

confidence: 96%

“…Proof The proof is by a Higgs bundle analogue of the Rees construction. The vector bundle version is discussed in [3,29,35]. First let us assume that we have a filtration (3.6) which is compatible with the Higgs field i.e.…”

Section: Upward Flows On Mmentioning

confidence: 99%

“…Within this context, mirror symmetry predicts that a BAA-brane should correspond to a BBB-brane on the mirror of M, which is to be understood as the statement that to a flat vector bundle on a complex Lagrangian on M there should exist a hyperholomorphic connection on a vector bundle over a hyperkähler submanifold of the mirror. A hyperholomorphic connection is a unitary connection whose curvature is of type (1, 1) with respect to each complex structure in the hyperkähler family of complex structures 3 . At this point in time, we have few constructions of hyperholomorphic connections on M so verifying the predictions is an important issue.…”

Section: Hyperholomorphic Connectionsmentioning

confidence: 99%

“…In Sect. 3 we determine which Higgs bundles belong to which upward and downward flows in the moduli space of Higgs bundles. In Sect.…”

mentioning

confidence: 99%

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Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Hausel

Hitchin

2022

Invent. math.

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We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. The main ingredients are the Bialynicki-Birula theory of $${\mathbb {C}}^*$$ C ∗ -actions on semiprojective varieties, $${\mathbb {C}}^*$$ C ∗ characters of indices of $${\mathbb {C}}^*$$ C ∗ -equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier–Mukai transform along the Hitchin fibration, hyperholomorphic structures on universal bundles and cominuscule Higgs bundles.

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“…However the integrality of m F E is not a complete obstruction for existence of very stable bundles as examples in Remark 5. 13 for type (1,3) in rank 4 show.…”

Section: For Generic a ∈ A The Intersection W +mentioning

confidence: 96%

Section: Upward Flows On Mmentioning

confidence: 99%

Section: Hyperholomorphic Connectionsmentioning

confidence: 99%

“…In Sect. 3 we determine which Higgs bundles belong to which upward and downward flows in the moduli space of Higgs bundles. In Sect.…”

mentioning

confidence: 99%

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Very stable Higgs bundles, equivariant multiplicity and mirror symmetry

Hausel

Hitchin

2022

Invent. math.

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“…For vector bundles this result is [6,Theorem 1.1] where some history is given. The general case can be deduced from this using the Tannaka formalism.…”

Section: D the Example Of Git-quotientsmentioning

confidence: 99%

Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves

Heinloth¹

2018

Épijournal De Géométrie Algébrique

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In these notes we reformulate the classical Hilbert-Mumford criterion for GIT stability in terms of algebraic stacks, this was independently done by Halpern-Leinster. We also give a geometric condition that guarantees the existence of separated coarse moduli spaces for the substack of stable objects. This is then applied to construct coarse moduli spaces for torsors under parahoric group schemes over curves. Comment: 37 pages

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