Comptes Rendus
no. 5
Mathematical analysis/Complex analysis
Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions
[Propriétés de semi-continuité des seuils log canoniques à poids de fonctions plurisousharmoniques toriques]

Présenté par : Jean-Pierre Demailly

Nguyen Xuan Hong1
1 Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Caugiay District, Hanoi, Viet Nam
Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 487-492.

Dans cette note, nous démontrons un théorème de semi-continuité pour certains seuils log canoniques à poids de fonctions plurisousharmoniques toriques.

In this note, we prove a semi-continuity theorem for certain weighted log canonical thresholds of toric plurisubharmonic functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.014
Nguyen Xuan Hong 1

1 Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Caugiay District, Hanoi, Viet Nam 
@article{CRMATH_2017__355_5_487_0,
     author = {Nguyen Xuan Hong},
     title = {Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {487--492},
     publisher = {Elsevier},
     volume = {355},
     number = {5},
     year = {2017},
     doi = {10.1016/j.crma.2017.04.014},
     language = {en},
}
TY  - JOUR
AU  - Nguyen Xuan Hong
TI  - Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 487
EP  - 492
VL  - 355
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crma.2017.04.014
LA  - en
ID  - CRMATH_2017__355_5_487_0
ER  - 
%0 Journal Article
%A Nguyen Xuan Hong
%T Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions
%J Comptes Rendus. Mathématique
%D 2017
%P 487-492
%V 355
%N 5
%I Elsevier
%R 10.1016/j.crma.2017.04.014
%G en
%F CRMATH_2017__355_5_487_0
Nguyen Xuan Hong. Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 487-492. doi : 10.1016/j.crma.2017.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.014/

[1] B. Berndtsson The extension theorem of Ohsawa–Takegoshi and the theorem of Donnelly–Fefferman, Ann. Inst. Fourier, Volume 46 (1996), pp. 1083-1094

[2] J.-P. Demailly; J. Kollár Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds, Ann. Sci. Éc. Norm. Supér. (4), Volume 34 (2001), pp. 525-556

[3] J.-P. Demailly; P.H. Hiep A sharp lower bound for the log canonical threshold, Acta Math., Volume 212 (2014), pp. 1-9

[4] Q. Guan; Z. Li Multiplier ideal sheaves associated with weights of log canonical threshold one, Adv. Math., Volume 302 (2016), pp. 40-47

[5] Q. Guan; X. Zhou A proof of Demailly's strong openness conjecture, Ann. of Math. (2), Volume 182 (2015), pp. 605-616

[6] Q. Guan; X. Zhou Effectiveness of Demailly's strong openness conjecture and related problems, Invent. Math., Volume 202 (2015) no. 2, pp. 635-676

[7] Q. Guan; X. Zhou Characterization of multiplier ideal sheaves with weights of Lelong number one, Adv. Math., Volume 285 (2015), pp. 1688-1705

[8] L.M. Hai; N.X. Hong; V.V. Hung A result on the comparison principle for the log canonical threshold of plurisubharmonic functions, Ann. Pol. Math., Volume 112 (2014), pp. 109-114

[9] P.H. Hiep A comparison principle for the log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013), pp. 441-443

[10] P.H. Hiep The weighted log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 283-288

[11] P.H. Hiep Continuity properties of certain weighted log canonical thresholds, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017), pp. 34-39

[12] P.H. Hiep Log canonical thresholds and Monge–Ampère masses, Math. Ann. (2017) | DOI

[13] P.H. Hiep; T. Tung The weighted log canonical thresholds of toric plurisubharmonic functions, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015) no. 2, pp. 127-131

[14] N.X. Hong; H. Viet Local property of maximal plurifinely plurisubharmonic functions, J. Math. Anal. Appl., Volume 441 (2016), pp. 586-592

[15] N.X. Hong; N.V. Trao; T.V. Thuy Convergence in capacity of plurisubharmonic functions with given boundary values, Int. J. Math., Volume 28 (2017) no. 3 (article ID: 1750018, 14 p)

[16] M. Klimek Pluripotential Theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1991

[17] T. Ohsawa; K. Takegoshi On the extension of L2 holomorphic functions, Math. Z., Volume 195 (1987), pp. 197-204

[18] A. Rashkovskii Extremal cases for the log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015) no. 1, pp. 21-24

[19] N.V. Trao; H. Viet; N.X. Hong Approximation of plurifinely plurisubharmonic functions, J. Math. Anal. Appl., Volume 450 (2017), pp. 1062-1075

Cité par Sources :

☆ This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2016.06. The author would like to thank the referees for valuable remarks which lead to the improvements of the exposition of the paper.

Commentaires - Politique