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On a Conjecture About Higgs Bundles and Some Inequalities
We briefly review an open conjecture about Higgs bundles that are semistable after pulling back to any curve, and prove it in the rank 2 case. We...
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Principal Higgs Bundles and Schottky Representations
Schottky representations are shown to be related to (A, B, A) branes in the moduli space of Principal Higgs bundles over a compact Riemann surface.
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Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
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...
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Poisson metrics and Higgs bundles over noncompact Kähler manifolds
In this paper, we study existence, uniqueness of Poisson metrics and K -analytically stability on flat bundles over noncompact Riemannian manifolds...
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ABELIANIZATION OF HIGGS BUNDLES FOR QUASI-SPLIT REAL GROUPS
We study the Hitchin map for G ℝ -Higgs bundles on a smooth curve, where G ℝ is a quasi-split real form of a complex reductive algebraic group G . By...
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On algebraic Chern classes of flat vector bundles
We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow...
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Representations of the fundamental group and Higgs bundles on singular integral curves
Let Y be an integral projective complex curve. To representations of the topological fundamental group of Y in the general linear group, we associate...
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Fixed Points of Involutions of G-Higgs Bundle Moduli Spaces over a Compact Riemann Surface with Classical Complex Structure Group
Let X be a compact and connected Riemann surface of genus g ≥ 2. In this paper, moduli spaces of Higgs bundles over X with structure group SL( n , ℂ),...
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Stratifications on the Moduli Space of Higgs Bundles
In this final chapter we review certain results on stratifications of the moduli space of Higgs bundles, performed with the invariants provided by...
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Moduli Spaces of Higgs Bundles – Old and New
We give an overview of the differential geometric and analytic aspects of Higgs bundles and their moduli spaces and highlight some of their...
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A Note on Bogomolov-Type Inequality for Semi-stable Parabolic Higgs Bundles
In this paper, we prove a Chern number inequality for Higgs bundles over some Kähler manifolds. As an application, we get the Bogomolov inequality...
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Logahoric Higgs torsors for a complex reductive group
In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G ,...
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The orbit type stratification of the moduli space of Higgs bundles
The moduli space of Higgs bundles can be constructed as a quotient of an infinite-dimensional space and hence admits an orbit type decomposition. In...
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Higgs bundles over foliation manifolds
In this paper, we consider the stability, semi-stability and canonical metric structures on transverse Higgs bundles over a class of foliation...
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On the Voevodsky motive of the moduli space of Higgs bundles on a curve
We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under...
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Analytically stable Higgs bundles on some non-Kähler manifolds
In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not...
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Moduli of rank 2 Higgs sheaves on elliptic surfaces
We study torsion-free, rank 2 Higgs sheaves on genus one fibered surfaces, (semi)stable with respect to suitable polarizations in the sense of...
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Stable Higgs bundles on ruled surfaces
Let π : X = ℙ C ( E ) → C be a ruled surface over an algebraically closed field k of characteristic 0, with a fixed polarization L on X . In this paper,...