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<p>Takuro Mochizuki (Transcations Am. Math. Soc. 373(1):551–596, 2020) recently studied the Kobayashi-Hitchin correspondence for analytically stable bundles over noncompact Kähler manifolds with possibly infinite volume as an extension of the work of Carlos Simpson (J. Am. Math. Soc. 1(4):867–918, 1988). The main target of this paper is to investigate the Kobayashi-Hitchin correspondence for analytically semi-stable bundles in the context of Takuro Mochizuki. More specifically, we prove the existence of approximate Hermitian-Yang-Mills structures and then establish a Bogomolov-Gieseker inequality. We also show the analytic semi-stability on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation> via <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-approximate Hermitian-Yang-Mills structures.</p>

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Kobayashi-Hitchin correspondence for analytically semi-stable bundles

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Di Wu,
  • Xi Zhang

摘要

Takuro Mochizuki (Transcations Am. Math. Soc. 373(1):551–596, 2020) recently studied the Kobayashi-Hitchin correspondence for analytically stable bundles over noncompact Kähler manifolds with possibly infinite volume as an extension of the work of Carlos Simpson (J. Am. Math. Soc. 1(4):867–918, 1988). The main target of this paper is to investigate the Kobayashi-Hitchin correspondence for analytically semi-stable bundles in the context of Takuro Mochizuki. More specifically, we prove the existence of approximate Hermitian-Yang-Mills structures and then establish a Bogomolov-Gieseker inequality. We also show the analytic semi-stability on \(\mathbb {C}\) C via \(L^1\) L 1 -approximate Hermitian-Yang-Mills structures.