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Toric plurisubharmonic functions and analytic adjoint ideal sheaves

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Abstract

In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the algebraic case studied by Howald. In the second part, almost entirely independent of the first one, we generalize the notion of the adjoint ideal sheaf used in algebraic geometry to the analytic setting. This enables us to give an analogue of Howald’s theorem for adjoint ideals attached to monomial ideals. Finally, using the local Ohsawa–Takegoshi–Manivel theorem, we prove the existence of the so-called generalized adjunction exact sequence, which enables us to recover a weak version of the global extension theorem of Manivel, for compact Kähler manifolds.

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References

  1. Boucksom S., Favre C., Jonsson M.: Valuations and plurisubharmonic singularities. Publ. RIMS Kyoto Univ. 44, 449–494 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  3. Demailly J.-P., Ein L., Lazarsfeld R.: A subadditivity property of multiplier ideals. Mich. Math. J. 48, 137–156 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    MATH  Google Scholar 

  7. Eisenstein, E.: Generalizations of the restriction theorem for multiplier ideals. J. Am. Math. Soc. arXiv:1001:2841 (2010)

    Google Scholar 

  8. Favre C., Jonsson M.: Valuations and multiplier ideals. J. Am. Math. Soc. 18, 655–684 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Howald J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353(7), 2665–2671 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lazarsfeld R.: Positivity in Algebraic Geometry II. Springer, New York (2004)

    Book  Google Scholar 

  11. McNeal, J.D., Zeytuncu, Y.E.: Multiplier ideals and integral closure of monomial ideals: an analytic approach. arXiv:1001.4983 (2010)

  12. Nadel A.: Multiplier ideal sheaves and existence of Kähler-Einsten metrics of positive scalar curvature. Ann. Math. 132, 549–596 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Roberts A.W., Varberg D.E.: Convex functions. Academic Press, New York (1973)

    MATH  Google Scholar 

  14. Takagi, S.: Adjoint ideals along closed subvarieties of higher codimension. arXiv:0711.2342 (2007)

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  1. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris, France

    Henri Guenancia

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  1. Henri Guenancia
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Correspondence to Henri Guenancia.

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Guenancia, H. Toric plurisubharmonic functions and analytic adjoint ideal sheaves. Math. Z. 271, 1011–1035 (2012). https://doi.org/10.1007/s00209-011-0900-0

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  • DOI: https://doi.org/10.1007/s00209-011-0900-0

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