scholarly journals Symplectic structure of the moduli space of flat connection on a Riemann surface

1995 ◽  
Vol 169 (1) ◽  
pp. 99-119 ◽  
Author(s):  
A. Yu. Alekseev ◽  
A. Z. Malkin
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Symplectic Structure ◽  
Flat Connection

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 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].

The Moduli Space of Yang–Mills Connections Over a Compact Surface

1997 ◽  
Vol 09 (01) ◽  
pp. 77-121 ◽  
Author(s):  
Ambar Sengupta
Keyword(s):  
Explicit Formula ◽  
Moduli Space ◽  
Symplectic Structure ◽  
Compact Surface ◽  
Gauge Groups ◽  
Yang Mills

Yang–Mills connections over closed oriented surfaces of genus ≥1, for compact connected gauge groups, are constructed explicitly. The resulting formulas for Yang–Mills connections are used to carry out a Marsden–Weinstein type procedure. An explicit formula is obtained for the resulting 2-form on the moduli space. It is shown that this 2-form provides a symplectic structure on appropriate subsets of the moduli space.

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

scholarly journals The dimension of the Hilbert space of geometric quantization of vortices on a Riemann surface

2017 ◽  
Vol 14 (10) ◽  
pp. 1750144
Author(s):  
Rukmini Dey ◽  
Saibal Ganguli
Keyword(s):  
Hilbert Space ◽  
Riemann Surface ◽  
Line Bundle ◽  
Euler Characteristic ◽  
Moduli Space ◽  
Geometric Quantization

In this paper, we calculate the dimension of the Hilbert space of Kähler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.

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