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A Note on the Weighted Log Canonical Threshold of Toric Plurisubharmonic Functions

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Ukrainian Mathematical Journal Aims and scope

We prove a semicontinuity theorem for a class of certain weighted log-canonical thresholds of toric plurisubharmonic functions.

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References

  1. 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).

  2. J.-P. Demailly, Complex Analytic and Differential Geometry; http://www-fourier.ujf-grenoble.fr/demailly/books.html (1997).

  3. J.-P. Demailly, “A numerical criterion for very ample line bundles,” J. Different. Geom., 37, 323–374 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  4. 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).

  5. J.-P. Demailly and P. H. Hiep, “A sharp lower bound for log canonical threshold,” Acta Math., 212, 1–9 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  6. P. H. Hiep, “The weighted log canonical threshold,” C. R. Math. Acad. Sci. Paris, 352, 283–288 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  7. P. H. Hiep, “Continuity properties of certain weighted log canonical thresholds,” C. R. Math. Acad. Sci. Paris, 355, 34–39 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  8. P. H. Hiep, “Log canonical thresholds and Monge–Ampère masses,” Math. Ann., 370, No. 1-2, 555–566 (2018).

    MathSciNet  MATH  Google Scholar 

  9. 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).

    Article  MathSciNet  MATH  Google Scholar 

  10. C. O. Kiselman, “Attenuating the singularities of plurisubharmonic functions,” Ann. Polon. Math., 60, 173–197 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  11. 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).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Rashkovskii, “Extremal cases for the log canonical threshold,” C. R. Math. Acad. Sci. Paris, 353, No. 1, 21–24 (2015).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Hoang Nhat Quy.

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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.

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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

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  • DOI: https://doi.org/10.1007/s11253-023-02201-x

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