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The Sharp Generalized Bogomolov Inequality

  • Chuanjing Zhang
  • Xi Zhang
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Abstract

Let (X,ω) be a compact Gauduchon and astheno-Kähler manifold. Using Lp-approximate critical Hermitian structures, we establish a sharp generalized Bogomolov inequality for holomorphic vector bundles on X, without any semistability assumption. We further characterize the equality case by studying the Hermitian-Yang-Mills flow. If equality holds, every Harder-Narasimhan-Seshadri filtration is by holomorphic subbundles, and its stable quotients admit projectively flat Hermitian metrics. If, in addition, the bundle is not ω-semistable, then X is projective.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026sharp,
  title = {{The Sharp Generalized Bogomolov Inequality}},
  author = {Chuanjing Zhang and Xi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24987},
  eprint = {2610.24987},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24987},
}
RIS
TY  - UNPB
TI  - The Sharp Generalized Bogomolov Inequality
AU  - Chuanjing Zhang
AU  - Xi Zhang
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.24987
UR  - https://arxiv.org/abs/2610.24987
AB  - Let (X,ω) be a compact Gauduchon and astheno-Kähler manifold. Using L^p-approximate critical Hermitian structures, we establish a sharp generalized Bogomolov inequality for holomorphic vector bundles on X, without any semistability assumption. We further characterize the equality case by studying the Hermitian-Yang-Mills flow. If equality holds, every Harder-Narasimhan-Seshadri filtration is by holomorphic subbundles, and its stable quotients admit projectively flat Hermitian metrics. If, in addition, the bundle is not ω-semistable, then X is projective.
ER  -