# Moduli Spaces of Generalized Hyperpolygons

@article{Rayan2020ModuliSO, title={Moduli Spaces of Generalized Hyperpolygons}, author={Steven Rayan and Laura P. Schaposnik}, journal={arXiv: Algebraic Geometry}, year={2020} }

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…

## 6 Citations

Hyperbolic band theory through Higgs bundles

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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…

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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…

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We construct explicit geometric models for moduli spaces of stable parabolic Higgs bundles on the Riemann sphere, in the case of rank two, four marked points, any degree, and arbitrary weights. The…

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