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Multiplier Submodule Sheaves and a problem of Lempert

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arxiv 2111.13452 v2 pith:3TYTZUZM submitted 2021-11-26 math.CV math.AGmath.DG

Zhuo Liu , Bo Xiao , Hui Yang , Xiangyu Zhou This is my paper · ORCID
classification math.CVmath.AGmath.DG
keywords nakanometricsbundleshermitianholomorphiclempertmultipliersemi-positive
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abstract

In this article, we establish an $L^2$ extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties of the multiplier submodule sheaves associated to Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing metrics based on Deng-Ning-Wang-Zhou's characterization of Nakano positivity.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Griffiths and Nakano positivity and Nakano-Nadel vanishing theorems for singular Hermitian metrics on complex spaces

    math.CV 2026-06 conditional novelty 7.0 of 10

    Nakano-positive singular Hermitian vector-bundle metrics on weakly pseudoconvex complex spaces imply vanishing of higher cohomology of the associated Grauert-Riemenschneider L2-canonical sheaf.

  2. An optimal $L^2$ extension for continuous $L^2$-optimal Hermitian metrics

    math.CV 2025-06 accept novelty 7.0 of 10

    Continuous L2-optimal Hermitian metrics satisfy an optimal L2 extension inequality with the logarithmic capacity constant, which implies they are Griffiths semi-positive.

  3. An Ohsawa-Takegoshi-type $L^2$ extension for upper semi-continuous $L^2$-optimal functions

    math.CV 2025-06 conditional novelty 5.0 of 10

    An L2 extension theorem is proved for upper semi-continuous L2-optimal functions using Lebesgue differentiation, yielding new characterizations and integrability results.

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