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PreprintarXiv licencearXiv

Yang-Mills-Higgs Limits of Reflexive Higgs Sheaves

  • Tianshu Jiang
  • Yijian Zhang
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Abstract

For stable Higgs bundles, Hermitian-Einstein metrics can be obtained as limits of the Yang-Mills-Higgs (Y-M-H) flow. We study the algebraic structure of subsequential limits of this flow for reflexive Higgs sheaves over compact Kähler manifolds, without assuming stability. We prove that the limiting reflexive Higgs sheaf is isomorphic to the double dual of the graded sheaf associated with the Harder-Narasimhan-Seshadri filtration of the initial sheaf.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026yangmillshiggs,
  title = {{Yang-Mills-Higgs Limits of Reflexive Higgs Sheaves}},
  author = {Tianshu Jiang and Yijian Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35742},
  eprint = {2610.35742},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35742},
}
RIS
TY  - UNPB
TI  - Yang-Mills-Higgs Limits of Reflexive Higgs Sheaves
AU  - Tianshu Jiang
AU  - Yijian Zhang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35742
UR  - https://arxiv.org/abs/2610.35742
AB  - For stable Higgs bundles, Hermitian-Einstein metrics can be obtained as limits of the Yang-Mills-Higgs (Y-M-H) flow. We study the algebraic structure of subsequential limits of this flow for reflexive Higgs sheaves over compact Kähler manifolds, without assuming stability. We prove that the limiting reflexive Higgs sheaf is isomorphic to the double dual of the graded sheaf associated with the Harder-Narasimhan-Seshadri filtration of the initial sheaf.
ER  -