Multiplier Submodule Sheaves and a problem of Lempert

2021/11/26 by Zhuo Liu, Liu, Zhuo, Xiao, Bo +4 · 2 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2111.13452

Abstract

In this article, we establish an L² 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.

Citations

• Bergman kernels and the pseudoeffectivity of relative canonical bundles

Cited by

• An optimal L² extension for continuous L²-optimal Hermitian metrics
• An Ohsawa-Takegoshi-type L² extension for upper semi-continuous L²-optimal functions

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