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.
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.
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Nguyen Xuan Hong 1
@article{CRMATH_2018__356_8_865_0, author = {Nguyen Xuan Hong}, title = {A note on the weighted log canonical thresholds of plurisubharmonic functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {865--869}, publisher = {Elsevier}, volume = {356}, number = {8}, year = {2018}, doi = {10.1016/j.crma.2018.06.003}, language = {en}, }
Nguyen Xuan Hong. A note on the weighted log canonical thresholds of plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 865-869. doi : 10.1016/j.crma.2018.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.06.003/
[1] Partial pluricomplex energy and integrability exponents of plurisubharmonic functions, Adv. Math., Volume 222 (2009), pp. 2036-2058
[2] A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982), pp. 1-40
[3] The general definition of the complex Monge–Ampère operator, Ann. Inst. Fourier, Volume 54 (2004), pp. 159-179
[4] Monge–Ampère operators, Lelong numbers and intersection theory, Complex Analysis and Geometry, Univ. Ser. Math., Plenum Press, New York, 1993, pp. 115-193
[5] A sharp lower bound for the log canonical threshold, Acta Math., Volume 212 (2014), pp. 1-9
[6] 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] Degenerate complex Monge–Ampère equations, EMS Tracts in Mathematics, vol. 26, European Mathematical Society (EMS), Zürich, Switzerland, 2017 (xxiv+472 p.)
[8] The weighted log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 283-288
[9] Log canonical thresholds and Monge–Ampère masses, Math. Ann., Volume 370 (2018), pp. 555-566
[10] 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] Pluripotential Theory, Clarendon Press – Oxford University Press, Oxford Science Publications, New York, 1991
[12] On the extension of holomorphic functions, Math. Z., Volume 195 (1987), pp. 197-204
[13] 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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