Multiplier submodule sheaves, 𝐿 <sup>2</sup> extension and a problem of Lempert
Abstract In this article, we establish an <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> L^{2} extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties for the multiplier submodule sheaves associated to such singular metrics. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing sequence of metrics based on Deng–Ning–Wang–Zhou’s characterization of Nakano positivity.
Authors
- Zhuo Liu (ORCID: https://orcid.org/0000-0002-7352-2016)
- Hui Yang
- Xiangyu Zhou
- Bo Xiao
Institutions
- Peking University (CN)
- Academy of Mathematics and Systems Science (CN)
- Institute of Mathematical Sciences (ES)
- Renmin University of China (CN)
Publication Details
- Journal
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Published
- 2026-03-02
- DOI
- https://doi.org/10.1515/crelle-2026-0009
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 0.00