Symmetry Integrability and Geometry Methods and Applications· 2026Q2
Moduli Spaces of Homologically Trivial Parabolic (Higgs) Bundles on the Projective Line and an Application to the Deligne-Simpson Problem
- 4citations
- Q2SCImago
- 2026year
Short summary
A new isomorphism connects moduli spaces of homologically trivial parabolic Higgs bundles on the projective line to star-shaped quiver varieties.
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Key points
- Establishes an isomorphism between moduli spaces of homologically trivial parabolic Higgs bundles on $\mathbb{P}^1$ and star-shaped quiver varieties.
- Applies this isomorphism to construct irreducible solutions for the nilpotent additive Deligne-Simpson problem.
- The construction of Deligne-Simpson solutions is contingent on explicit numerical assumptions.
AI-generated from the title and abstract; the full text is not read.
Abstract
We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on $\mathbb{P}^1$ and the quiver variety associated to a star-shaped quiver. As an application, we give a Hitchin-theoretic construction of irreducible solutions to the nilpotent additive Deligne-Simpson problem under explicit numerical assumptions.
The authors' abstract, as published at the source. Symmetry Integrability and Geometry Methods and Applications, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics