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<p>In this article, we give a survey about the strong openness and stability properties of the multiplier ideal sheaves associated to plurisubharmonic functions. We also present generalizations and new proofs of some established theorems. Specifically, we offer a uniform version of Skoda’s integrability theorem formulated by Zeriahi, and elaborate on semicontinuity properties for weighted log canonical thresholds. Furthermore, we conclude by presenting various formulations of stability theorems about the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> multiplier ideal sheaves.</p>

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Properties of Multiplier Ideal Sheaves and Applications

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Bo Xiao,
  • Xiangyu Zhou

摘要

In this article, we give a survey about the strong openness and stability properties of the multiplier ideal sheaves associated to plurisubharmonic functions. We also present generalizations and new proofs of some established theorems. Specifically, we offer a uniform version of Skoda’s integrability theorem formulated by Zeriahi, and elaborate on semicontinuity properties for weighted log canonical thresholds. Furthermore, we conclude by presenting various formulations of stability theorems about the \(L^p\) L p multiplier ideal sheaves.