no. G11
Analyse et géométrie complexes
New Properties of Multiplier Submodule Sheaves
[Nouvelles Propriétés des Faisceaux de Sous-modules Multiplicateurs]
Liu, Zhuo1, 2 ; Yang, Hui3, 2 ; Zhou, Xiangyu4 
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, Tome 360 (2022) no. G11, 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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
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 
@article{CRMATH_2022__360_G11_1205_0,
     author = {Liu, Zhuo and Yang, Hui and Zhou, Xiangyu},
     title = {New {Properties} of {Multiplier} {Submodule} {Sheaves}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1205--1212},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G11},
     year = {2022},
     doi = {10.5802/crmath.334},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.334/}
}
TY  - JOUR
AU  - Liu, Zhuo
AU  - Yang, Hui
AU  - Zhou, Xiangyu
TI  - New Properties of Multiplier Submodule Sheaves
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 1205
EP  - 1212
VL  - 360
IS  - G11
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.334/
DO  - 10.5802/crmath.334
LA  - en
ID  - CRMATH_2022__360_G11_1205_0
ER  - 
%0 Journal Article
%A Liu, Zhuo
%A Yang, Hui
%A Zhou, Xiangyu
%T New Properties of Multiplier Submodule Sheaves
%J Comptes Rendus. Mathématique
%D 2022
%P 1205-1212
%V 360
%N G11
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.334/
%R 10.5802/crmath.334
%G en
%F CRMATH_2022__360_G11_1205_0
Liu, Zhuo; Yang, Hui; Zhou, Xiangyu. New Properties of Multiplier Submodule Sheaves. Comptes Rendus. Mathématique, Tome 360 (2022) no. G11, pp. 1205-1212. doi : 10.5802/crmath.334. http://www.numdam.org/articles/10.5802/crmath.334/

[1] Berndtsson, Bo The openness conjecture and complex Brunn-Minkowski inequalities, Complex geometry and dynamics. The Abel symposium 2013, (Fornæss, John Erik et al., eds.) (Abel Symposia), Volume 10, Springer, 2015, pp. 29-44 | DOI | MR | Zbl

[2] de Cataldo, Mark Andrea A. Singular hermitian metrics on vector bundles, J. Reine Angew. Math., Volume 502 (1998), pp. 93-122 | MR | Zbl

[3] Demailly, Jean-Pierre Multiplier ideal sheaves and analytic methods in algebraic geometry, School on Vanishing Theorems and Effective Results in Algebraic Geometry (ICTP Lecture Notes), Volume 6, The Abdus Salam International Centre for Theoretical Physics, 2001, pp. 1-148 | MR | Zbl

[4] Demailly, Jean-Pierre; Kollár, János Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds, Ann. Sci. Éc. Norm. Supér., Volume 34 (2001) no. 4, pp. 525-556 | DOI | Numdam | Zbl

[5] Demailly, Jean-Pierre; Peternell, Thomas; Schneider, Michael Pseudo-effective line bundles on compact Kähler manifolds, Int. J. Math., Volume 12 (2001) no. 6, pp. 689-741 | DOI | Zbl

[6] Deng, Fusheng; Ning, Jiafu; Wang, Zhiwei; Zhou, Xiangyu Positivity of holomorphic vector bundles in terms of L p -conditions of ∂ ¯ (2020) online published in Math. Ann. (2022), p. 1-33, https://arxiv.org/abs/2001.01762v1

[7] Favre, Charles; Jonsson, Mattias Valuations and multiplier ideals, J. Am. Math. Soc., Volume 18 (2005) no. 3, pp. 655-684 | DOI | MR | Zbl

[8] Guan, Qi’an A sharp effectiveness result of Demailly’s strong openness conjecture, Adv. Math., Volume 348 (2019), pp. 51-80 | DOI | MR | Zbl

[9] Guan, Qi’an; Li, Zhenqian; Zhou, Xiangyu Estimation of weighted L 2 norm related to Demailly’s strong openness conjecture (2016) (to appear in Chinese Annals of Math., Series B, https://arxiv.org/abs/1603.05733v1)

[10] Guan, Qi’an; Zhou, Xiangyu Effectiveness of Demailly’s strong openness conjecture and related problems, Invent. Math., Volume 202 (2015) no. 2, pp. 635-676 | DOI | MR | Zbl

[11] Guan, Qi’an; Zhou, Xiangyu A proof of Demailly’s strong openness conjecture, Ann. Math., Volume 182 (2015) no. 2, pp. 605-616 | DOI | MR | Zbl

[12] Hiep, Pham Hoang The weighted log canonical threshold, C. R. Math. Acad. Sci. Paris, Volume 352 (2014) no. 4, pp. 283-288 | DOI | MR | Zbl

[13] Inayama, Takahiro Nakano positivity of singular hermitian metrics and vanishing theorems of Demailly–Nadel–Nakano type, Algebr. Geom., Volume 9 (2022) no. 1, pp. 69-92 | DOI | MR | Zbl

[14] Jonsson, Mattias; Mustaţă, Mircea Valuations and asymptotic invariants for sequences of ideals, Ann. Inst. Fourier, Volume 62 (2012) no. 6, pp. 2145-2209 | DOI | Numdam | MR | Zbl

[15] Lempert, László Modules of square integrable holomorphic germs, Analysis meets geometry. The Mikael Passare memorial volume (Trends in Mathematics), Springer, 2017, pp. 311-333 | DOI | Zbl

[16] Liu, Zhou; Yang, Hui; Zhou, Xiangyu On the Multiplier Submodule Sheaves Associated to Singular Nakano Semi-positive Metrics (2021) (https://arxiv.org/abs/2111.13452)

[17] Raufi, Hossein Singular hermitian metrics on holomorphic vector bundles, Ark. Mat., Volume 53 (2015) no. 2, pp. 359-382 | DOI | MR | Zbl

[18] Wade, William R. The bounded convergence theorem, Am. Math. Mon., Volume 81 (1974) no. 4, pp. 387-389 | DOI | MR | Zbl

[19] Yau, Shing-Tung On the pseudonorm project of birational classification of algebraic varieties, Geometry and analysis on manifolds (Progress in Mathematics), Volume 608, Springer, 2015, pp. 327-339 | Zbl

Cité par Sources :