Dans cet article, nous montrons comment appliquer la version originelle du théorème d'extension de Ohsawa et Takegoshi à la base standard d'un faisceau d'idéaux multiplicateurs associé à une fonction plurisousharmonique. Ceci nous permet de redémontrer la conjecture d'ouverture forte et d'obtenir une version effective du théorème de semi-continuité pour les seuils log-canoniques pondérés.
In this note, we show how to apply the original -extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong openness conjecture and to obtain an effective version of the semicontinuity theorem for weighted log canonical thresholds.
@article{CRMATH_2014__352_4_283_0, author = {Pham Hoang Hiep}, title = {The weighted log canonical threshold}, journal = {Comptes Rendus. Math\'ematique}, pages = {283--288}, publisher = {Elsevier}, volume = {352}, number = {4}, year = {2014}, doi = {10.1016/j.crma.2014.02.010}, language = {en}, }
Pham Hoang Hiep. The weighted log canonical threshold. Comptes Rendus. Mathématique, Volume 352 (2014) no. 4, pp. 283-288. doi : 10.1016/j.crma.2014.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.02.010/
[1] The division algorithm and the Hilbert scheme, Havard University, June 1982 (Ph.D. Thesis)
[2] The openness conjecture for plurisubharmonic functions, 2013 | arXiv
[3] Relations among analytic functions I, Ann. Inst. Fourier, Volume 37 (1987), pp. 187-239
[4] Uniformization of analytic spaces, J. Amer. Math. Soc., Volume 2 (1989), pp. 801-836
[5] Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds, 2012 | arXiv
[6] Monge–Ampère operators, Lelong numbers and intersection theory (V. Ancona; A. Silva, eds.), Complex Analysis and Geometry, Univ. Series in Math., Plenum Press, New York, 1993
[7] A numerical criterion for very ample line bundles, J. Differential Geom., Volume 37 (1993), pp. 323-374
[8] Complex analytic and differential geometry http://www-fourier.ujf-grenoble.fr/demailly/books.html
[9] A sharp lower bound for the log canonical threshold, Acta Math., Volume 212 (2014), pp. 1-9 | DOI
[10] Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds, Ann. Sci. École Norm. Sup., Volume 34 (2001), pp. 525-556
[11] Commutative Algebra with a View Toward Algebraic Geometry, Grad. Texts in Math., vol. 150, Springer, New York, 1995
[12] Valuations and multiplier ideals, J. Amer. Math. Soc., Volume 18 (2005), pp. 655-684
[13] Bounds for log canonical thresholds with applications to birational rigidity, Math. Res. Lett., Volume 10 (2003), pp. 219-236
[14] Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties, Duke Math. J., Volume 152 (2010), pp. 93-114
[15] Théorème de division et stabilité en géométrie analytique locale, Ann. Inst. Fourier, Volume 29 (1979), pp. 107-184
[16] Optimal constant problem in the -extension theorem, C. R. Acad. Sci. Paris, Ser. I, Volume 350 (2012), pp. 753-756
[17] Strong openness conjecture and related problems for plurisubharmonic functions, 2014 | arXiv
[18] The log canonical threshold of holomorphic functions, Int. J. Math., Volume 23 (2012)
[19] A comparison principle for the log canonical threshold, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013), pp. 441-443
[20] Valuations and asymptotic invariants for sequences of ideals, Ann. Inst. Fourier, Volume 62 (2012), pp. 2145-2209
[21] An algebraic approach to the openness conjecture of Demailly and Kollár, J. Inst. Math. Jussieu, Volume 13 (2014), pp. 119-144
[22] Attenuating the singularities of plurisubharmonic functions, Ann. Polon. Math., Volume 60 (1994), pp. 173-197
[23] Multiplier ideal sheaves and Kähler–Einstein metrics of positive scalar curvature, Ann. Math., Volume 132 (1990), pp. 549-596
[24] On the extension of holomorphic functions, Math. Z., Volume 195 (1987), pp. 197-204
[25] On a conjecture of Demailly and Kollar, Asian J. Math., Volume 4 (2000), pp. 221-226
[26] Sous-ensembles analytiques d'ordre fini ou infini dans , Bull. Soc. Math. France, Volume 100 (1972), pp. 353-408
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