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.

scholarly journals On the Geometry of the Moduli Space of Real Binary Octics

2011 ◽  
Vol 63 (4) ◽  
pp. 755-797 ◽  
Author(s):  
Kenneth C. K. Chu
Keyword(s):  
Moduli Space ◽  
Dense Subset ◽  
Connected Components ◽  
Complex Conjugate ◽  
Open Dense Subset ◽  
Reflection Groups ◽  
Arithmetic Subgroup ◽  
Real Analytic Manifold ◽  
Real Analytic ◽  
Real Hyperbolic Space

Abstract The moduli space of smooth real binary octics has five connected components. They para- metrize the real binary octics whose defining equations have 0, … , 4 complex-conjugate pairs of roots respectively. We show that each of these five components has a real hyperbolic structure in the sense that each is isomorphic as a real-analytic manifold to the quotient of an open dense subset of 5- dimensional real hyperbolic space by the action of an arithmetic subgroup of Isom. These subgroups are commensurable to discrete hyperbolic reflection groups, and the Vinberg diagrams of the latter are computed.

ON MODULI SPACE OF HIGGS Gp(2n, ℂ)-BUNDLES OVER A RIEMANN SURFACE

2010 ◽  
Vol 07 (02) ◽  
pp. 311-322
Author(s):  
INDRANIL BISWAS ◽  
SARBESWAR PAL
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Hilbert Scheme ◽  
Symplectic Form ◽  
Cotangent Bundle ◽  
Symplectic Structure ◽  
Topological Type ◽  
Total Space ◽  
The Other ◽  
Complex Variety

Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by KX. Let [Formula: see text] denote the moduli space of semistable Higgs Gp (2n, ℂ)-bundles over X of fixed topological type. The complex variety [Formula: see text] has a natural holomorphic symplectic structure. On the other hand, for any ℓ ≥ 1, the Liouville symplectic from on the total space of KX defines a holomorphic symplectic structure on the Hilbert scheme Hilb ℓ(KX) parametrizing the zero-dimensional subschemes of KX. We relate the symplectic form on Hilb ℓ(KX) with the symplectic form on [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 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 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 Genericity of the multibump dynamics for almost periodic Duffing-like systems

1999 ◽  
Vol 129 (5) ◽  
pp. 885-901 ◽  
Author(s):  
Francesca Alessio ◽  
Paolo Caldiroli ◽  
Piero Montecchiari
Keyword(s):  
Variational Methods ◽  
Dense Subset ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Almost Periodic

In this paper we consider ‘slowly’ oscillating perturbations of almost periodic Duffing-like systems, i.e. systems of the form ü = u − (a(t) + α(wt))W′(u), t ∈ ℝ, u ∈ ℝN, where W ∈ C2N(ℝN, ℝ) is superquadratic and a and α are positive and almost periodic. By variational methods, we prove that if w > 0 is small enough, then the system admits a multibump dynamics. As a consequence we get that the system ü = u − a(t)W′(u), t ∈ ℝ, u ∈ ℝN, admits multibump solutions whenever a belongs to an open dense subset of the set of positive almost periodic continuous functions.

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