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arXiv · 2111.13452

Multiplier Submodule Sheaves and a problem of Lempert

Zhuo Liu·Bo Xiao·Hui Yang·Xiangyu Zhou
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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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Zhuo Liu, Bo Xiao, Hui Yang, Xiangyu Zhou. 2021-11-26. Multiplier Submodule Sheaves and a problem of Lempert. https://arxiv.org/abs/2111.13452

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