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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

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

  • Xueqing Wen1
  1. 1Chongqing University of Technology, P.R. China
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Abstract

We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on ℙ1 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.

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Cite

BibTeXRIS
BibTeX
@article{wen2026moduli,
  title = {{Moduli Spaces of Homologically Trivial Parabolic (Higgs) Bundles on the Projective Line and an Application to the Deligne-Simpson Problem}},
  author = {Xueqing Wen},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.101},
  url = {https://sigma-journal.com/2026/101/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Moduli Spaces of Homologically Trivial Parabolic (Higgs) Bundles on the Projective Line and an Application to the Deligne-Simpson Problem
AU  - Xueqing Wen
PY  - 2026
DA  - 2026/10/23
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.101
UR  - https://sigma-journal.com/2026/101/
AB  - We establish an isomorphism between the moduli space of homologically trivial parabolic (Higgs) bundles on 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.
SN  - 1815-0659
ER  -