Comptes Rendus
Analyse et géométrie complexes
New Properties of Multiplier Submodule Sheaves
[Nouvelles Propriétés des Faisceaux de Sous-modules Multiplicateurs]
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1205-1212.

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.

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.

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DOI : 10.5802/crmath.334
Classification : 32U05, 32E10, 32L10, 32Q10, 14F18, 14C30, 53C55
Zhuo Liu 1, 2 ; Hui Yang 3, 2 ; Xiangyu Zhou 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Zhuo Liu; Hui Yang; Xiangyu Zhou. New Properties of Multiplier Submodule Sheaves. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1205-1212. doi : 10.5802/crmath.334. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.334/

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