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Star-Shaped Nakajima Quiver Varieties, Parabolic Higgs Bundle Moduli Spaces, and their Holomorphic Symplectic Structures
[Submitted on 22 Jun 2026] · 2026-06-23 · via math updates on arXiv.org

Mathematics > Differential Geometry

arXiv:2606.23369 (math)

[Submitted on 22 Jun 2026]

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Abstract:In this paper, we consider two classes of hyperkähler manifolds: moduli spaces of central-Levi parabolic Higgs bundles on the punctured sphere and star-shaped Nakajima quiver varieties. We produce a map $\mathcal T$ from a given star-shaped quiver variety $\mathcal X$ to a central-Levi parabolic Higgs bundle moduli space $\mathcal M$. We verify that $\mathcal T$ preserves stability and we show that it is a homeomorphism onto the locus of Higgs bundles with trivial underlying holomorphic structure. We then prove our main theorem: that $\mathcal T$ identifies the natural holomorphic symplectic structures on the two spaces. This theorem generalizes work by Biswas, Florentino, Godinho, Mandini from the rank 2, full flag, strongly parabolic case to arbitrary rank, partial flag, and weakly parabolic cases -- namely, those whose Higgs field residues project to the centers of their respective Levi subalgebras.

Submission history

From: Arya Yae [view email]
[v1] Mon, 22 Jun 2026 14:04:23 UTC (41 KB)

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