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Toric plurisubharmonic functions and analytic adjoint ideal sheaves. (English) Zbl 1255.32014

The paper is divided on two independent parts. The main result of the first part is a precise description of the multiplier ideal sheaves associated to a toric plurisubharmonic (psh) function. Recall that a psh toric function is a psh function that is pointwise invariant under the compact unit torus \(T^n\). The description given by the author generalizes a result of J. A. Howald [Trans. Am. Math. Soc. 353, No. 7, 2665–2671 (2001; Zbl 0979.13026)] for the algebraic case.
In the begining of the second part and after introducing the anologue of the algebraic adjoint ideal sheaf in the analytic setting, the author proves a generalization of Howald’s theorem for the adjoint ideals attached to monomial ideals. Next, the author uses the local Ohsawa-Takegoshi-Manivel theorem to prove his second main result, namely the existence of the adjunction exact sequence in the analytic setting. As an application, a weak version of the global extension theorem of Manivel is given, for compact Kähler manifolds.

MSC:

32U05 Plurisubharmonic functions and generalizations
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14F18 Multiplier ideals

Citations:

Zbl 0979.13026
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References:

[1] Boucksom S., Favre C., Jonsson M.: Valuations and plurisubharmonic singularities. Publ. RIMS Kyoto Univ. 44, 449–494 (2008) · Zbl 1146.32017 · doi:10.2977/prims/1210167334
[2] Demailly, J.-P., Bertin, J., Illusie, L., Peters, C.: Introduction à la théorie de Hodge. Panorama et Synthèses, vol. 3. Soc. Math. de France (1996) · Zbl 0849.14002
[3] Demailly J.-P., Ein L., Lazarsfeld R.: A subadditivity property of multiplier ideals. Mich. Math. J. 48, 137–156 (2000) · Zbl 1077.14516 · doi:10.1307/mmj/1030132712
[4] Demailly, J.-P.: Complex Analytic and Algebraic Geometry. In preparation
[5] Demailly, J.-P.: Multiplier ideal sheaves and analytic methods in algebraic geometry. In: Lecture Notes, vol. 6. ICTP (2001) · Zbl 1102.14300
[6] Demailly J.-P., Kollár J.: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Ann. Sci. École Norm. Sup. 34, 525–556 (2001) · Zbl 0994.32021
[7] Eisenstein, E.: Generalizations of the restriction theorem for multiplier ideals. J. Am. Math. Soc. arXiv:1001:2841 (2010)
[8] Favre C., Jonsson M.: Valuations and multiplier ideals. J. Am. Math. Soc. 18, 655–684 (2005) · Zbl 1075.14001 · doi:10.1090/S0894-0347-05-00481-9
[9] Howald J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353(7), 2665–2671 (2001) · Zbl 0979.13026 · doi:10.1090/S0002-9947-01-02720-9
[10] Lazarsfeld R.: Positivity in Algebraic Geometry II. Springer, New York (2004) · Zbl 1093.14500
[11] McNeal, J.D., Zeytuncu, Y.E.: Multiplier ideals and integral closure of monomial ideals: an analytic approach. arXiv:1001.4983 (2010) · Zbl 1246.13041
[12] Nadel A.: Multiplier ideal sheaves and existence of Kähler-Einsten metrics of positive scalar curvature. Ann. Math. 132, 549–596 (1990) · Zbl 0731.53063 · doi:10.2307/1971429
[13] Roberts A.W., Varberg D.E.: Convex functions. Academic Press, New York (1973) · Zbl 0271.26009
[14] Takagi, S.: Adjoint ideals along closed subvarieties of higher codimension. arXiv:0711.2342 (2007) · Zbl 1193.14024
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