Complex analysis and geometry
New Properties of Multiplier Submodule Sheaves
Comptes Rendus. Mathématique, Volume 360 (2022) no. G11, pp. 1205-1212.

In this note, we establish the strong openness and stability property of multiplier submodule sheaves associated to singular Nakano semi-positive metrics on holomorphic vector bundles, which generalizes the same properties for multiplier ideal sheaves associated to pseudo-effective line bundles.

Dans cette note, nous établissons la conjecture forte d’ouverture et la stabilité des faisceaux de sous-modules multiplicateurs associés aux métriques semi-positives de Nakano singulières sur les fibrés vectoriels holomorphes, ce qui généralise les mêmes propriétés pour les faisceaux d’idéaux multiplicateurs associés aux fibrés en droites pseudo-effectifs.

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DOI: 10.5802/crmath.334
Classification: 32U05, 32E10, 32L10, 32Q10, 14F18, 14C30, 53C55
Liu, Zhuo 1, 2; Yang, Hui 3, 2; Zhou, Xiangyu 4

1 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences,Beijing 100190, P. R. China
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
3 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, P. R. China
4 Institute of Mathematics, Academy of Mathematics and Systems Sciences, Beijing 100190, P. R. China
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Liu, Zhuo; Yang, Hui; Zhou, Xiangyu. New Properties of Multiplier Submodule Sheaves. Comptes Rendus. Mathématique, Volume 360 (2022) no. G11, pp. 1205-1212. doi : 10.5802/crmath.334. http://www.numdam.org/articles/10.5802/crmath.334/

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