scholarly journals Brauer Group of Moduli of Higgs Bundles and Connections

2018 ◽  
pp. 387-398
Author(s):  
David Baraglia ◽  
Indranil Biswas ◽  
Laura P. Schaposnik
Keyword(s):  
Riemann Surface ◽  
Algebraic Group ◽  
Moduli Spaces ◽  
Compact Riemann Surface ◽  
Brauer Group ◽  
Higgs Bundles ◽  
Smooth Locus

Given a compact Riemann surface X and a semi-simple affine algebraic group G defined over C, there are moduli spaces of Higgs bundles and of connections associated to (X, G). The chapter computes the Brauer group of the smooth locus of these varieties.

scholarly journals INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS

2021 ◽  
pp. 1-40
Author(s):  
Mirko Mauri
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Compact Riemann Surface ◽  
Character Variety ◽  
Degree Zero ◽  
Surface Groups ◽  
Higgs Bundles ◽  
Character Varieties ◽  
Rank 2

Abstract For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compact Riemann surface C and of the moduli space of G-Higgs bundles on C of degree zero. We derive several results concerning the P=W conjectures for these singular moduli spaces.

scholarly journals On moduli spaces of Hitchin pairs

2011 ◽  
Vol 151 (3) ◽  
pp. 441-457 ◽  
Author(s):  
INDRANIL BISWAS ◽  
PETER B. GOTHEN ◽  
MARINA LOGARES
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Isomorphism Class ◽  
Compact Riemann Surface ◽  
List Type ◽  
Holomorphic Line Bundle ◽  
Type Number ◽  
Additional Hypothesis

AbstractLetXbe a compact Riemann surfaceXof genus at–least two. Fix a holomorphic line bundleLoverX. Letbe the moduli space of Hitchin pairs (E, φ ∈H0(End0(E) ⊗L)) overXof rankrand fixed determinant of degreed. The following conditions are imposed:(i)deg(L) ≥ 2g−2,r≥ 2, andL⊗rKX⊗r;(ii)(r, d) = 1; and(iii)ifg= 2 thenr≥ 6, and ifg= 3 thenr≥ 4.We prove that that the isomorphism class of the varietyuniquely determines the isomorphism class of the Riemann surfaceX. Moreover, our analysis shows thatis irreducible (this result holds without the additional hypothesis on the rank for low genus).

scholarly journals Moduli space of branched superminimal immersions of a compact Riemann surface into S4

1999 ◽  
Vol 66 (1) ◽  
pp. 32-50 ◽  
Author(s):  
Bonaventure Loo
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Compact Riemann Surface ◽  
Projective Varieties ◽  
Fibre Products ◽  
Dimension 2 ◽  
Path Connected

AbstractIn this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max {2g, g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.

scholarly journals Nilpotent Higgs Bundles and the Hodge Metric on the Calabi–Yau Moduli

2021 ◽  
Author(s):  
Qiongling Li
Keyword(s):  
Riemann Surface ◽  
Upper Bound ◽  
Compact Riemann Surface ◽  
Higgs Bundles ◽  
Topological Information ◽  
Nilpotent Matrices ◽  
Sectional Curvatures ◽  
Hodge Metric

Abstract We study an algebraic inequality for nilpotent matrices and show some interesting geometric applications: (i) obtaining topological information for nilpotent polystable Higgs bundles over a compact Riemann surface; (ii) obtaining a sharp upper bound of the holomorphic sectional curvatures of the period domain and the Hodge metric on the Calabi–Yau moduli.

Moduli spaces of bundles on an abelian variety

2017 ◽  
Vol 14 (02) ◽  
pp. 1750030
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Abelian Variety ◽  
Moduli Spaces ◽  
Character Variety ◽  
Higgs Bundles ◽  
Connected Component ◽  
Trivial Bundle

Let [Formula: see text] be a complex abelian variety and [Formula: see text] a complex reductive affine algebraic group. We describe the connected component, containing the trivial bundle, of the moduli spaces of topologically trivial principal [Formula: see text]-bundles and [Formula: see text]-Higgs bundles on [Formula: see text]. We also describe the moduli spaces of [Formula: see text]-connections and the [Formula: see text]-character variety for [Formula: see text].

scholarly journals BIRATIONAL EQUIVALENCE OF HIGGS MODULI

2005 ◽  
Vol 16 (04) ◽  
pp. 365-386
Author(s):  
MRIDUL MEHTA
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Compact Riemann Surface ◽  
Holomorphic Section ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
Birational Equivalence

In this paper, we study triples of the form (E, θ, ϕ) over a compact Riemann surface, where (E, θ) is a Higgs bundle and ϕ is a global holomorphic section of the Higgs bundle. Our main result is an description of a birational equivalence which relates geometrically the moduli space of Higgs bundles of rank r and degree d to the moduli space of Higgs bundles of rank r-1 and degree d.

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.

Sign in / Sign up

Export Citation Format

Share Document