Potential theory/Complex analysis
A note on the weighted log canonical thresholds of plurisubharmonic functions
[Une note sur les seuils log canoniques à poids de fonctions pluri-sous-harmoniques]
Comptes Rendus. Mathématique, Tome 356 (2018) no. 8, pp. 865-869.

Dans cette note, nous donnons une caractérisation des seuils log canoniques à poids de fonctions pluri-sous-harmoniques. En guise d'application, nous démontrons une inégalité pour les seuils log canoniques à poids et les masses de Monge–Ampère.

In this note, we give a characterization for the weighted log canonical thresholds of plurisubharmonic functions. As an application, we prove an inequality for weighted log canonical thresholds and Monge–Ampère masses.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.06.003
Hong, Nguyen Xuan 1

1 Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Caugiay District, Hanoi, Vietnam
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Hong, Nguyen Xuan. A note on the weighted log canonical thresholds of plurisubharmonic functions. Comptes Rendus. Mathématique, Tome 356 (2018) no. 8, pp. 865-869. doi : 10.1016/j.crma.2018.06.003. http://www.numdam.org/articles/10.1016/j.crma.2018.06.003/

[1] Åhag, P.; Cegrell, U.; Kołodziej, S.; Hiep, P.H.; Zeriahi, A. Partial pluricomplex energy and integrability exponents of plurisubharmonic functions, Adv. Math., Volume 222 (2009), pp. 2036-2058

[2] Bedford, E.; Taylor, B.A. A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982), pp. 1-40

[3] Cegrell, U. The general definition of the complex Monge–Ampère operator, Ann. Inst. Fourier, Volume 54 (2004), pp. 159-179

[4] Demailly, J.-P. Monge–Ampère operators, Lelong numbers and intersection theory, Complex Analysis and Geometry, Univ. Ser. Math., Plenum Press, New York, 1993, pp. 115-193

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

[6] Demailly, J.-P.; Kollár, J. 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

[7] Guedj, V.; Zeriahi, A. Degenerate complex Monge–Ampère equations, EMS Tracts in Mathematics, vol. 26, European Mathematical Society (EMS), Zürich, Switzerland, 2017 (xxiv+472 p.)

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

[9] Hiep, P.H. Log canonical thresholds and Monge–Ampère masses, Math. Ann., Volume 370 (2018), pp. 555-566

[10] Hong, N.X. Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017), pp. 487-492

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

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

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

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