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References
Åhag, P., Cegrell, U., Czyz, R., Pham, H.H.: Monge-Ampère measures on pluripolar sets. J. Math. Pures Appl. 92, 613–627 (2009)
Åhag, P., Cegrell, U., Kołodziej, S., Pham, H.H., Zeriahi, A.: Partial pluricomplex energy and integrability exponents of plurisubharmonic functions. Adv. Math. 222, 2036–2058 (2009)
Berndtsson, B.: The openness conjecture and complex Brunn-Minkowski inequalities. Comp. Geom. Dyn. 10, 29–44 (2015)
Blocki, Z.: The domain of definition of the complex Monge-Ampère operator. Am. J. Math. 128, 519–530 (2006)
Blocki, Z.: Suita conjecture and the Ohsawa-Takegoshi extension theorem. Invent. Math. 193, 149–158 (2013)
Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge-Ampère equation. Invent. Math. 37, 1–44 (1976)
Bedford, E., Taylor, B.A.: A new capacity for plurisubharmonic functions. Acta Math. 149, 1–41 (1982)
Cegrell, U.: Pluricomplex energy. Acta Math. 180, 187–217 (1998)
Cegrell, U.: The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier 54, 159–179 (2004)
Corti, A.: Factoring birational maps of threefolds after Sarkisov. J. Alg. Geom. 4, 223–254 (1995)
Corti, A.: Singularities of linear systems and \(3\)-fold birational geometry. Explic. Bir. Geom. 281, 259–312 (2000)
Demailly, J.-P.: Nombres de Lelong généralisés, théorèmes d’intégralité et d’analyticité. Acta Math. 159, 153–169 (1987)
Demailly, J.-P.: Regularization of closed positive currents and Intersection Theory. J. Alg. Geom. 1, 361–409 (1992)
Demailly, J.-P.: Monge-Ampère operators, Lelong numbers and intersection theory, Complex Analysis and Geometry, Univ. Series in Math., edited by V. Ancona and A. Silva, Plenum Press, New-York, (1993)
Demailly, J.-P.: Estimates on Monge-Ampère operators derived from a local algebra inequality, in: Complex Analysis and Digital geometry, Proceedings of the Kiselmanfest 2006, Acta Universitatis Upsaliensis, (2009)
Demailly, J.-P.: Extension of holomorphic functions defined on non reduced analytic subvarieties, arXiv:1510.05230 [math.CV] (2015)
Demailly, J.-P., Pham, H.H.: A sharp lower bound for the log canonical threshold. Acta Math. 212, 1–9 (2014)
Demailly, J.-P., Kollár, J.: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Ann. Sci. Ecol. Norm. Sup. 34(4), 525–556 (2001)
de Fernex, T., Ein, T., Mustaţǎ, M.: Bounds for log canonical thresholds with applications to birational rigidity. Math. Res. Lett. 10, 219–236 (2003)
de Fernex, T., Ein, L., Mustaţǎ, M.: Multiplicities and log canonical thresholds. J. Alg. Geom. 13, 603–615 (2004)
Guan, Q., Zhou, X.: A proof of Demailly’s strong openness conjecture. Ann. Math. 182, 605–616 (2015)
Guan, Q., Zhou, X.: Effectiveness of Demailly’s strong openness conjecture and related problems. Invent. Math. 202, 635–676 (2015)
Guan, Q., Zhou, X.: Multiplier ideal sheaves, jumping numbers, and the restriction formula, arXiv:1504.04209 [math.CV] (2015)
Howald, J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353, 2665–2671 (2001)
Kim, D.: Themes on Non-analytic Singularities of Plurisubharmonic Functions, Volume 144 of the series Springer Proceedings in Mathematics and Statistics, 197–206 (2015)
Kiselman, C.O.: Un nombre de Lelong raffiné, Séminaire d’Analyse Complexe et Géométrie 1985-87, Fac. Sci. Tunis & Fac. Sci. Tech. Monastir, 61–70 (1987)
Kiselman, C.O.: Attenuating the singularities of plurisubharmonic functions. Ann. Polon. Math. 60, 173–197 (1994)
Matsumura, S.: A Nadel vanishing theorem for metrics with minimal singularities on big line bundles. Adv. Math. 280, 188–207 (2015)
Ohsawa, T., Takegoshi, K.: On the extension of \(L^2\) holomorphic functions. Math. Zeit. 195, 197–204 (1987)
Pham, H.H.: The weighted log canonical threshold. C. R. Math. 352, 283–288 (2014)
Rashkovskii, A.: Extremal cases for the log canonical threshold. C. R. Math. 353, 21–24 (2014)
Skoda, H.: Sous-ensembles analytiques d’ordre fini ou infini dans \({\mathbb{C}}^n\). Bull. Soc. Math. Fr. 100, 353–408 (1972)
Acknowledgements
The author is grateful to Professor Jean-Pierre Demailly, Dr. Nguyen Ngoc Cuong and the anonymous reviewers for valuable comments, which helped to improve the paper. This paper was partly written when the author was visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for support and providing a fruitful research environment and hospitality. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2014.01.
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Communicated by Ngaiming Mok.