In this article, we compute the weighted log canonical thresholds of toric plurisubharmonic functions, i.e. convex increasing functions of the logarithms of the absolute values of their complex arguments.
Dans cet article, nous calculons les seuils log canoniques pondérés des fonctions plurisous-harmoniques toriques, c'est-à-dire s'exprimant comme des fonctions convexes croissantes des logarithmes des modules de leurs arguments complexes.
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Pham Hoang Hiep 1; Trinh Tung 2
@article{CRMATH_2015__353_2_127_0, author = {Pham Hoang Hiep and Trinh Tung}, title = {The weighted log canonical thresholds of toric plurisubharmonic functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {127--131}, publisher = {Elsevier}, volume = {353}, number = {2}, year = {2015}, doi = {10.1016/j.crma.2014.11.005}, language = {en}, }
Pham Hoang Hiep; Trinh Tung. The weighted log canonical thresholds of toric plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 127-131. doi : 10.1016/j.crma.2014.11.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.005/
[1] The openness conjecture and complex Brunn–Minkowski inequalities, Proceedings of Abel Symposium 2013, 2014 (in press) | arXiv
[2] J.-P. Demailly, Monge–Ampère operators, Lelong numbers and intersection theory, in: V. Ancona, A. Silva (Eds.), Complex Analysis and Geometry, in: University Series in Mathematics, Plenum Press, New York, 1993.
[3] Complex analytic and differential geometry http://www-fourier.ujf-grenoble.fr/demailly/books.html
[4] Bounds for log canonical thresholds with applications to birational rigidity, Math. Res. Lett., Volume 10 (2003), pp. 219-236
[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., Volume 34 (2001), pp. 525-556
[7] Valuations and asymptotic invariants for sequences of ideals, Ann. Inst. Fourier, Volume 62 (2012), pp. 2145-2209
[8] Multiplier ideal sheaves and Kähler–Einstein metrics of positive scalar curvature, Ann. Math., Volume 132 (1990), pp. 549-596
[9] A comparison principle for the log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013), pp. 441-443
[10] The weighted log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 352 (2014), pp. 283-288
[11] Multiplier ideals of monomial ideals, Trans. Amer. Math. Soc., Volume 353 (2001), pp. 2665-2671
[12] Attenuating the singularities of plurisubharmonic functions, Ann. Pol. Math., Volume 60 (1994), pp. 173-197
[13] Sous-ensembles analytiques d'ordre fini ou infini dans , Bull. Soc. Math. Fr., Volume 100 (1972), pp. 353-408
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