Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 2 min ago
PreprintarXiv licencearXiv

Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces

  • Keshu Zhou
Open at sourcePDFDOICite

Abstract

We develop a geometric way to uniformly carry out Hörmander's L2-estimates for Hermitian-Yang-Mills connections with bounded energy on Kähler surfaces. We then show the Uhlenbeck convergence of smooth HYM connections on Kähler surfaces can be realized as algebraic convergence inside an analytic flat family. As applications, we prove a continuity theorem for smoothable families and a boundedness result for μ-semistable sheaves with fixed topology. We also discuss potential applications for the moduli problem.

Related

  1. Hermitian Connections with Parallel Torsion and the Fino--Vezzoni Conjecture
    Shuwen Chen, Fangyang Zheng
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Hermitian connections with parallel torsion and constant holomorphic sectional curvature
    Shuwen Chen, Fangyang Zheng
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Kähler-like characteristic connections
    Luigi Marigliano
    HALPreprintCC BY-NC-SA 4.0Full textGeometry & topologyHAL
  4. Non-Hermitian Yang--Mills Connections with Vanishing Chern Classes
    Guangzhen Ren
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class
    Nikita Klemyatin
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{zhou2026algebraic,
  title = {{Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces}},
  author = {Keshu Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01221},
  eprint = {2610.01221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01221},
}
RIS
TY  - UNPB
TI  - Algebraic limits of Hermitian-Yang-Mills connections on Kähler surfaces
AU  - Keshu Zhou
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01221
UR  - https://arxiv.org/abs/2610.01221
AB  - We develop a geometric way to uniformly carry out Hörmander's L^2-estimates for Hermitian-Yang-Mills connections with bounded energy on Kähler surfaces. We then show the Uhlenbeck convergence of smooth HYM connections on Kähler surfaces can be realized as algebraic convergence inside an analytic flat family. As applications, we prove a continuity theorem for smoothable families and a boundedness result for μ-semistable sheaves with fixed topology. We also discuss potential applications for the moduli problem.
ER  -