Log canonical thresholds and Monge-Ampère masses

1. Åhag, P., Cegrell, U., Czyz, R., Pham, H.H.: Monge-Ampère measures on pluripolar sets. J. Math. Pures Appl. 92, 613–627 (2009)

   Article  MathSciNet  MATH  Google Scholar 

2. 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)

   Article  MathSciNet  MATH  Google Scholar 

3. Berndtsson, B.: The openness conjecture and complex Brunn-Minkowski inequalities. Comp. Geom. Dyn. 10, 29–44 (2015)

   Article  MathSciNet  MATH  Google Scholar 

4. Blocki, Z.: The domain of definition of the complex Monge-Ampère operator. Am. J. Math. 128, 519–530 (2006)

   Article  MATH  Google Scholar 

5. Blocki, Z.: Suita conjecture and the Ohsawa-Takegoshi extension theorem. Invent. Math. 193, 149–158 (2013)

   Article  MathSciNet  MATH  Google Scholar 

6. Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge-Ampère equation. Invent. Math. 37, 1–44 (1976)

   Article  MathSciNet  MATH  Google Scholar 

7. Bedford, E., Taylor, B.A.: A new capacity for plurisubharmonic functions. Acta Math. 149, 1–41 (1982)

   Article  MathSciNet  MATH  Google Scholar 

8. Cegrell, U.: Pluricomplex energy. Acta Math. 180, 187–217 (1998)

   Article  MathSciNet  MATH  Google Scholar 

9. Cegrell, U.: The general definition of the complex Monge-Ampère operator. Ann. Inst. Fourier 54, 159–179 (2004)

   Article  MathSciNet  MATH  Google Scholar 

10. Corti, A.: Factoring birational maps of threefolds after Sarkisov. J. Alg. Geom. 4, 223–254 (1995)

    MathSciNet  MATH  Google Scholar 

11. Corti, A.: Singularities of linear systems and \(3\)-fold birational geometry. Explic. Bir. Geom. 281, 259–312 (2000)

    MathSciNet  MATH  Google Scholar 

12. Demailly, J.-P.: Nombres de Lelong généralisés, théorèmes d’intégralité et d’analyticité. Acta Math. 159, 153–169 (1987)

    Article  MathSciNet  MATH  Google Scholar 

13. Demailly, J.-P.: Regularization of closed positive currents and Intersection Theory. J. Alg. Geom. 1, 361–409 (1992)

    MathSciNet  MATH  Google Scholar 

14. 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)

15. 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)

16. Demailly, J.-P.: Extension of holomorphic functions defined on non reduced analytic subvarieties, arXiv:1510.05230 [math.CV] (2015)

17. Demailly, J.-P., Pham, H.H.: A sharp lower bound for the log canonical threshold. Acta Math. 212, 1–9 (2014)

    Article  MathSciNet  MATH  Google Scholar 

18. 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)

    Article  MATH  Google Scholar 

19. de Fernex, T., Ein, T., Mustaţǎ, M.: Bounds for log canonical thresholds with applications to birational rigidity. Math. Res. Lett. 10, 219–236 (2003)

    Article  MathSciNet  MATH  Google Scholar 

20. de Fernex, T., Ein, L., Mustaţǎ, M.: Multiplicities and log canonical thresholds. J. Alg. Geom. 13, 603–615 (2004)

    Article  MathSciNet  MATH  Google Scholar 

21. Guan, Q., Zhou, X.: A proof of Demailly’s strong openness conjecture. Ann. Math. 182, 605–616 (2015)

    Article  MathSciNet  MATH  Google Scholar 

22. Guan, Q., Zhou, X.: Effectiveness of Demailly’s strong openness conjecture and related problems. Invent. Math. 202, 635–676 (2015)

    Article  MathSciNet  MATH  Google Scholar 

23. Guan, Q., Zhou, X.: Multiplier ideal sheaves, jumping numbers, and the restriction formula, arXiv:1504.04209 [math.CV] (2015)

24. Howald, J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353, 2665–2671 (2001)

    Article  MathSciNet  MATH  Google Scholar 

25. Kim, D.: Themes on Non-analytic Singularities of Plurisubharmonic Functions, Volume 144 of the series Springer Proceedings in Mathematics and Statistics, 197–206 (2015)

26. 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)

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

    Article  MathSciNet  MATH  Google Scholar 

28. Matsumura, S.: A Nadel vanishing theorem for metrics with minimal singularities on big line bundles. Adv. Math. 280, 188–207 (2015)

    Article  MathSciNet  MATH  Google Scholar 

29. Ohsawa, T., Takegoshi, K.: On the extension of \(L^2\) holomorphic functions. Math. Zeit. 195, 197–204 (1987)

    Article  MATH  Google Scholar 

30. Pham, H.H.: The weighted log canonical threshold. C. R. Math. 352, 283–288 (2014)

    Article  MathSciNet  MATH  Google Scholar 

31. Rashkovskii, A.: Extremal cases for the log canonical threshold. C. R. Math. 353, 21–24 (2014)

    Article  MathSciNet  MATH  Google Scholar 

32. Skoda, H.: Sous-ensembles analytiques d’ordre fini ou infini dans \({\mathbb{C}}^n\). Bull. Soc. Math. Fr. 100, 353–408 (1972)

    Article  MathSciNet  MATH  Google Scholar 

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