no. G6
Analyse et géométrie complexes
A note on the weighted log canonical threshold
Nguyen Van Phu1
1 Faculty of Natural Sciences, Electric Power University, Hanoi, Vietnam
Comptes Rendus. Mathématique, Tome 361 (2023) no. G6, pp. 969-971

In this paper, we introduce and study a set relative to singularities of plurisubharmonic functions. We prove that this set is countable under the condition h>0 on 𝔹∖{0}.

Reçu le :
Révisé le :
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DOI : 10.5802/crmath.456
Classification : 32U05, 32U15, 32U40, 32W20

Nguyen Van Phu 1

1 Faculty of Natural Sciences, Electric Power University, Hanoi, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A note on the weighted log canonical threshold},
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Nguyen Van Phu. A note on the weighted log canonical threshold. Comptes Rendus. Mathématique, Tome 361 (2023) no. G6, pp. 969-971. doi: 10.5802/crmath.456

[1] Demailly, Jean-Pierre Monge-Ampère operators, Lelong Numbers and Intersection theory, Complex analysis and geometry (The University Series in Mathematics), Plenum Press, 1993, pp. 115-193 | DOI | Zbl

[2] Demailly, Jean-Pierre; Hiệp, Phạm Hoàng A sharp lower bound for the log canonical threshold, Acta Math., Volume 212 (2014) no. 1, pp. 1-9 | DOI | Zbl | MR

[3] Demailly, Jean-Pierre; Kollár, János Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds, Ann. Sci. Éc. Norm. Supér., Volume 34 (2001) no. 4, pp. 525-556 | DOI | Numdam | Zbl

[4] de Fernex, Tommaso; Ein, Lawrence; Mustaţă, Mircea Bounds for log canonical thresholds with applications to birational rigidity, Math. Res. Lett., Volume 10 (2003) no. 2-3, pp. 219-236 | Zbl | MR

[5] de Fernex, Tommaso; Ein, Lawrence; Mustaţă, Mircea Shokurov’s ACC Conjecture for log canonical thresholds on smooth varieties, Duke Math. J., Volume 152 (2010) no. 1, pp. 93-114 | MR | Zbl

[6] Hai, Le Mau; Hiệp, Phạm Hoàng; Tung, Trinh Estimates of level sets of holomorphic functions and applications to the weighted log canonical thresholds, J. Geom. Anal. (2021), pp. 3783-3819 | MR | Zbl

[7] Hiệp, Phạm Hoàng A comparison principle for log canonical threshold, C. R. Acad. Sci. Paris, Volume 351 (2013) no. 11-12, pp. 441-443 | DOI | Zbl | MR

[8] Hiệp, Phạm Hoàng The weighted log canonical threshold, C. R. Acad. Sci. Paris, Volume 352 (2014) no. 4, pp. 283-288 | DOI | MR | Numdam | Zbl

[9] Hiệp, Phạm Hoàng Continuity properties of certain weighted log canonical thresholds, C. R. Acad. Sci. Paris, Volume 355 (2017) no. 1, pp. 34-39 | DOI | MR | Numdam | Zbl

[10] Hiệp, Phạm Hoàng Log canonical thresholds and Monge–Ampère masses, Math. Ann., Volume 370 (2018) no. 1-2, pp. 556-566 | Zbl

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