SIGMA 22 (2026), 101, 24 pages      arXiv:2101.01913      https://doi.org/10.3842/SIGMA.2026.101

Moduli Spaces of Homologically Trivial Parabolic (Higgs) Bundles on the Projective Line and an Application to the Deligne-Simpson Problem

Xueqing Wen
Chongqing University of Technology, No. 69, Hongguang Avenue, Chongqing, 400054, P.R. China

Received January 21, 2026, in final form October 14, 2026; Published online October 23, 2026

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.

Key words: parabolic Higgs bundles; quiver varieties; Deligne-Simpson problem.

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