Moduli Spaces of Generalized Hyperpolygons

  title={Moduli Spaces of Generalized Hyperpolygons},
  author={Steven Rayan and Laura P. Schaposnik},
  journal={arXiv: Algebraic Geometry},
We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the Lie algebra of a compact group and the other in its complexification. To such data, we associate an explicit meromorphic Higgs bundle on a genus-$g$ Riemann surface, where $g$ is the number of loops in the comet, thereby embedding the Nakajima quiver variety… 

Figures from this paper

Hyperbolic band theory through Higgs bundles

Geometric Models and Variation of Weights on Moduli of Parabolic Higgs Bundles over the Riemann Sphere: a Case Study

  • Claudio Meneses
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2022
. We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and

The Kapustin–Witten equations and nonabelian Hodge theory

Arising from a topological twist of $\mathcal{N} = 4$ super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametrized by

All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces

We demonstrate that the linear quotient singularity for the exceptional subgroup G in Sp(4,C) of order 32 is isomorphic to an affine quiver variety for a 5-pointed star-shaped quiver. This allows us



Construction of Instantons


In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean

The construction of ALE spaces as hyper-Kähler quotients

On decrit la construction d'une famille particuliere de 4-varietes hyper-Kahler: les espaces asymptotiquement localement euclidiens ALE. On decrit une 4-variete de Riemann avec juste une extremite

Electric-Magnetic Duality And The Geometric Langlands Program

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are

Asymptotic geometry of the moduli space of parabolic SL(2,C)-higgs bundles

  • arXiv preprint arXiv :
  • 2001

Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles

Given a generic stable strongly parabolic $SL(2,\mathbb{C})$-Higgs bundle $(\mathcal{E}, \varphi)$, we describe the family of harmonic metrics $h_t$ for the ray of Higgs bundles $(\mathcal{E}, t

Generalized B-Opers

Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper

On the cohomology ring of the hyperKähler analogue of the polygon spaces

Quasi-parabolic Higgs bundles and null hyperpolygon spaces

The moduli space of quasi-parabolic Higgs bundles over a compact Riemann surface is introduced and a natural involution is considered, studying its fixed point locus when theinline-formula content-type is considered.


. In “Quantization of Hitchin’s Integrable System and Hecke Eigen-sheaves”, Beilinson and Drinfeld introduced the “very good” property for a smooth complex equidimensional stack. They prove that for