We prove a semicontinuity theorem for a class of certain weighted log-canonical thresholds of toric plurisubharmonic functions.
References
J.-P. Demailly, “Monge–Ampère operators, Lelong numbers and intersection theory,” in: V. Ancona and A. Silva (Eds.), Complex Analysis and Geometry, Univ. Ser. Math., Plenum, New York (1993).
J.-P. Demailly, Complex Analytic and Differential Geometry; http://www-fourier.ujf-grenoble.fr/demailly/books.html (1997).
J.-P. Demailly, “A numerical criterion for very ample line bundles,” J. Different. Geom., 37, 323–374 (1993).
J.-P. Demailly and J. Kollár, “Semicontinuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds,” Ann. Sci. Ècole Norm. Sup. (4), 34, No. 4, 525–556 (2001).
J.-P. Demailly and P. H. Hiep, “A sharp lower bound for log canonical threshold,” Acta Math., 212, 1–9 (2014).
P. H. Hiep, “The weighted log canonical threshold,” C. R. Math. Acad. Sci. Paris, 352, 283–288 (2014).
P. H. Hiep, “Continuity properties of certain weighted log canonical thresholds,” C. R. Math. Acad. Sci. Paris, 355, 34–39 (2017).
P. H. Hiep, “Log canonical thresholds and Monge–Ampère masses,” Math. Ann., 370, No. 1-2, 555–566 (2018).
P. H. Hiep and T. Tung, “The weighted log canonical thresholds of toric plurisubharmonic functions,” C. R. Math. Acad. Sci. Paris, 353, No. 2, 127–131 (2015).
C. O. Kiselman, “Attenuating the singularities of plurisubharmonic functions,” Ann. Polon. Math., 60, 173–197 (1994).
D. H. Phong and J. Sturm, “Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions,” Ann. Math. (2), 152, 277–329 (2000).
A. Rashkovskii, “Extremal cases for the log canonical threshold,” C. R. Math. Acad. Sci. Paris, 353, No. 1, 21–24 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 2, pp. 287–292, February, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i2.6768.
Rights and permissions
About this article
Cite this article
Quy, H.N. A Note on the Weighted Log Canonical Threshold of Toric Plurisubharmonic Functions. Ukr Math J 75, 328–334 (2023). https://doi.org/10.1007/s11253-023-02201-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-023-02201-x