scholarly journals The orbit type stratification of the moduli space of Higgs bundles

2021 ◽  
Author(s):  
Yue Fan
Keyword(s):  
Moduli Space ◽  
Higgs Bundles ◽  
Orbit Type

scholarly journals On the Voevodsky motive of the moduli space of Higgs bundles on a curve

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Characteristic Zero ◽  
Rational Point ◽  
Triangulated Category ◽  
Higgs Bundles ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
De Rham

AbstractWe 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 the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

scholarly journals Principal co-Higgs bundles on ℙ1

2020 ◽  
Vol 63 (2) ◽  
pp. 512-530 ◽  
Author(s):  
Indranil Biswas ◽  
Oscar García-Prada ◽  
Jacques Hurtubise ◽  
Steven Rayan
Keyword(s):  
Moduli Space ◽  
Borel Subgroup ◽  
Algebraic Groups ◽  
Projective Line ◽  
Higgs Bundles ◽  
Complex Projective Line ◽  
Theoretic Characterization ◽  
Complex Projective

AbstractFor complex connected, reductive, affine, algebraic groups G, we give a Lie-theoretic characterization of the semistability of principal G-co-Higgs bundles on the complex projective line ℙ1 in terms of the simple roots of a Borel subgroup of G. We describe a stratification of the moduli space in terms of the Harder–Narasimhan type of the underlying bundle.

scholarly journals QUANTIZATION OF A MODULI SPACE OF PARABOLIC HIGGS BUNDLES

2004 ◽  
Vol 15 (09) ◽  
pp. 907-917 ◽  
Author(s):  
INDRANIL BISWAS ◽  
AVIJIT MUKHERJEE
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Symplectic Form ◽  
Dense Subset ◽  
Projective Structure ◽  
Open Dense Subset ◽  
Higgs Bundles ◽  
Smooth Variety ◽  
Structure Formula

Let [Formula: see text] be a moduli space of stable parabolic Higgs bundles of rank two over a Riemann surface X. It is a smooth variety defined over [Formula: see text] equipped with a holomorphic symplectic form. Fix a projective structure [Formula: see text] on X. Using [Formula: see text], we construct a quantization of a certain Zariski open dense subset of the symplectic variety [Formula: see text].

Mirror Symmetry with Branes by Equivariant Verlinde Formulas

2018 ◽  
pp. 189-218
Author(s):  
Tamás Hausel ◽  
Anton Mellit ◽  
Du Pei
Keyword(s):  
Functional Equation ◽  
Riemann Surface ◽  
Moduli Space ◽  
Mirror Symmetry ◽  
Higgs Bundles ◽  
Exterior Powers

This chapter finds an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL2 Higgs moduli space on a Riemann surface. On one side of the agreement, components of the Lagrangian brane of U(1,1) Higgs bundles, whose mirror was proposed by Hitchin to be certain even exterior powers of the hyperholomorphic Dirac bundle on the SL2 Higgs moduli space, are present. The agreement arises from a mysterious functional equation. This gives strong computational evidence for Hitchin’s proposal.

Model Higgs bundles in exceptional components of the Sp(4, ℝ)-character variety

2021 ◽  
pp. 2150067
Author(s):  
Georgios Kydonakis
Keyword(s):  
Elliptic Operator ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Higgs Bundle ◽  
Character Variety ◽  
Topological Invariants ◽  
Higgs Bundles ◽  
Connected Sum ◽  
Anosov Representations

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the [Formula: see text]-Hitchin equations using the linearization of a relevant elliptic operator. The construction can be used to provide model Higgs bundles in all the [Formula: see text] exceptional components of the maximal [Formula: see text]-Higgs bundle moduli space, which correspond to components solely consisting of Zariski dense representations. This also allows a comparison between the invariants for maximal Higgs bundles and the topological invariants for Anosov representations constructed by Guichard and Wienhard.

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