Comptes Rendus
no. 1
Complex analysis
Continuity properties of certain weighted log canonical thresholds
[Propriétés de continuité de certains seuils log canoniques pondérés]

Présenté par : Jean-Pierre Demailly

Pham Hoang Hiep1
1 Hanoi Institute of Mathematics, VAST, Viet Nam
Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 34-39.

Dans cette note, nous démontrons un théorème de semi-continuité pour une classe de seuils log-canoniques pondérés et obtenons des résultats connexes pour des restrictions de fonctions plurisubharmoniques à des sous-espaces k-dimensionnels et pour des faisceaux d'idéaux multiplicateurs.

In this note, we prove a semicontinuity theorem for a class of weighted log canonical thresholds, and obtain some related results for restrictions of plurisubharmonic functions to k-dimensional subspaces and for multiplier ideal sheaves.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.005
Pham Hoang Hiep 1

1 Hanoi Institute of Mathematics, VAST, Viet Nam 
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Pham Hoang Hiep. Continuity properties of certain weighted log canonical thresholds. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 34-39. doi : 10.1016/j.crma.2016.11.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.005/

[1] B. Berndtsson The openness conjecture for plurisubharmonic functions, Complex Geometry and Dynamics: The Abel Symposium, 2013

[2] Z. Blocki Suita conjecture and the Ohsawa–Takegoshi extension theorem, Invent. Math., Volume 193 (2013), pp. 149-158

[3] J.-P. Demailly Monge–Ampère operators, Lelong numbers and intersection theory (V. Ancona; A. Silva, eds.), Complex Analysis and Geometry, University Series in Mathematics, Plenum Press, New York, 1993

[4] J.-P. Demailly A numerical criterion for very ample line bundles, J. Differential Geom., Volume 37 (1993), pp. 323-374

[5] J.-P. Demailly Complex analytic and differential geometry http://www-fourier.ujf-grenoble.fr/demailly/books.html

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

[7] 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

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

[9] Q. Guan; X. Zhou Multiplier ideal sheaves, jumping numbers, and the restriction formula | arXiv

[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 Log canonical thresholds and Monge–Ampère masses | arXiv

[12] C.O. Kiselman Attenuating the singularities of plurisubharmonic functions, Ann. Pol. Math., Volume 60 (1994), pp. 173-197

[13] A. Nadel Multiplier ideal sheaves and Kähler–Einstein metrics of positive scalar curvature, Ann. of Math. (2), Volume 132 (1990), pp. 549-596

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

[15] D.H. Phong; J. Sturm Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions, Ann. of Math. (2), Volume 152 (2000), p. 277329

[16] H. Skoda Sous-ensembles analytiques d'ordre fini ou infini dans Cn, Bull. Soc. Math. Fr., Volume 100 (1972), pp. 353-408

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