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<p>Let <i>X</i> be a compact Kähler manifold of dimension <i>n</i>, and let <i>T</i> be a closed positive (1,&#xa0;1)-current in a nef cohomology class on <i>X</i>. We establish an optimal upper bound for the volume of components of Lelong upper level sets of <i>T</i> in terms of cohomology classes of non-pluripolar self-products of <i>T</i>.</p>

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Volumes of components of Lelong upper level sets II

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月13日

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  • Shuang Su,
  • Duc-Viet Vu

摘要

Let X be a compact Kähler manifold of dimension n, and let T be a closed positive (1, 1)-current in a nef cohomology class on X. We establish an optimal upper bound for the volume of components of Lelong upper level sets of T in terms of cohomology classes of non-pluripolar self-products of T.