An explicit description of the symplectic structure of moduli spaces of flat connections

1994 ◽  
Vol 35 (10) ◽  
pp. 5338-5353 ◽  
Author(s):  
Christopher King ◽  
Ambar Sengupta
Keyword(s):  
Moduli Spaces ◽  
Symplectic Structure ◽  
Explicit Description ◽  
Flat Connections

scholarly journals Moduli spaces of orthogonal and symplectic bundles over an algebraic curve

2008 ◽  
Vol 144 (3) ◽  
pp. 721-733 ◽  
Author(s):  
Olivier Serman
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Algebraic Curve ◽  
Vector Bundles ◽  
Explicit Description ◽  
Representation Space ◽  
Classical Groups ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Polynomial Invariants

AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.

scholarly journals On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

2004 ◽  
Vol 56 (6) ◽  
pp. 1228-1236 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Chiu-Chu Melissa Liu
Keyword(s):  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Orientable Surface ◽  
Equivalence Classes ◽  
Nonorientable Surface ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Compact Orientable Surface ◽  
Simply Connected

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

scholarly journals RELATIVE UNITARY RZ-SPACES AND THE ARITHMETIC FUNDAMENTAL LEMMA

2020 ◽  
pp. 1-61
Author(s):  
Andreas Mihatsch
Keyword(s):  
Linear Algebra ◽  
Moduli Spaces ◽  
Level Structure ◽  
Explicit Description ◽  
Lower Dimension ◽  
Fundamental Lemma ◽  
Divisible Groups ◽  
Moduli Problems

We prove a comparison isomorphism between certain moduli spaces of $p$ -divisible groups and strict ${\mathcal{O}}_{K}$ -modules (RZ-spaces). Both moduli problems are of PEL-type (polarization, endomorphism, level structure) and the difficulty lies in relating polarized $p$ -divisible groups and polarized strict ${\mathcal{O}}_{K}$ -modules. We use the theory of relative displays and frames, as developed by Ahsendorf, Lau and Zink, to translate this into a problem in linear algebra. As an application of these results, we verify new cases of the arithmetic fundamental lemma (AFL) of Wei Zhang: The comparison isomorphism yields an explicit description of certain cycles that play a role in the AFL. This allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension.

On Some Geometric Invariants Associated to the Space of Flat Connections on an Open Space

1996 ◽  
Vol 39 (2) ◽  
pp. 169-177
Author(s):  
I. Biswas ◽  
K. Guruprasad
Keyword(s):  
Moduli Space ◽  
Symplectic Structure ◽  
Open Space ◽  
Geometric Invariant ◽  
Flat Connections ◽  
Geometric Invariants ◽  
Marked Surface

AbstractA geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

scholarly journals GEOMETRY OF MODULI SPACES OF FLAT BUNDLES ON PUNCTURED SURFACES

1998 ◽  
Vol 09 (01) ◽  
pp. 63-73 ◽  
Author(s):  
PHILIP A. FOTH
Keyword(s):  
Riemann Surface ◽  
Conjugacy Class ◽  
Moduli Spaces ◽  
Flat Connections ◽  
Rational Singularities ◽  
Take All

For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.

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