New Properties of Multiplier Submodule Sheaves

Zhuo Liu; Hui Yang; Xiangyu Zhou

doi:10.5802/crmath.334

Analyse et géométrie complexes

New Properties of Multiplier Submodule Sheaves
[Nouvelles Propriétés des Faisceaux de Sous-modules Multiplicateurs]

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

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1205-1212.

Résumé
Abstract

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.

Reçu le : 2021-11-27
Révisé le : 2022-01-18
Accepté le : 2022-01-19
Publié le : 2022-12-08

DOI : 10.5802/crmath.334

Classification : 32U05, 32E10, 32L10, 32Q10, 14F18, 14C30, 53C55

Affiliations des auteurs :

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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     author = {Zhuo Liu and Hui Yang and Xiangyu Zhou},
     title = {New {Properties} of {Multiplier} {Submodule} {Sheaves}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1205--1212},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.334},
     language = {en},
}

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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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