Work

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

Year: 2026

Type: article

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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2026.101

Author: Xueqing Wen

Institution: Chongqing University of Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Chongqing University of Technology

OpenAlex ID: W7223399443