manuscripta mathematica

, Volume 130, Issue 1, pp 45–61 | Cite as

Log canonical thresholds of binomial ideals

Article

Abstract

We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.

Mathematics Subject Classification (2000)

13A35 14B05 90C05 

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References

  1. 1.
    Blickle M., Mustaţǎ M., Smith K.E.: Discreteness and rationality of F-thresholds. Michigan Math. J. 57, 43–61 (2008)CrossRefMathSciNetGoogle Scholar
  2. 2.
    de Fernex, T., Mustaţǎ, M.: Limits of log canonical thresholds, arXiv:0710.4978. Ann. Sci. Ecole Norm. Sup. (to appear)Google Scholar
  3. 3.
    Eisenbud D., Strumfels B.: On binomial ideals. Duke Math. J. 84, 1–45 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Hara N., Yoshida K.: A generalization of tight closure and multiplier ideals. Trans. Am. Math. Soc. 355, 3143–3174 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hironaka H.: Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. Math. (2) 79, 109–203 (1964)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Hironaka H.: Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. Math. (2) 79, 205–326 (1964)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Howald J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353, 2665–2671 (2001)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Howald, J.: Multiplier ideals of sufficiently general polynomials, arXiv:math. AG/0303203 (2003, preprint)Google Scholar
  9. 9.
    Lazarsfeld, R.: Positivity in algebraic geometry II. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. In: A Series of Modern Surveys in Mathematics, vol. 49. Springer, Berlin (2004)Google Scholar
  10. 10.
    Mustaţǎ, M., Takagi, S., Watanabe, K.-i.: F-thresholds and Bernstein-Sato polynomials. In: European Congress of Mathematics, pp. 341–364. European Matheematical Society, Zürich (2005)Google Scholar
  11. 11.
    Röhrl, N.: Binomial regular sequences and S-matrices, Diplomarbeit, Universität Regensburg, available at http://www.iadm.uni-stuttgart.de/LstAnaMPhy/Roehrl/ (1998)
  12. 12.
    Shibuta, T.: An algorithm for computing multiplier ideals, arXiv:0807.4302 (2008, preprint)Google Scholar
  13. 13.
    Takagi S.: Formulas for multiplier ideals on singular varieties. Am. J. Math. 128, 1345–1362 (2006)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Takagi S., Watanabe K.-i.: On F-pure thresholds. J. Algebra 282(1), 278–297 (2004)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsRikkyo UniversityTokyoJapan
  2. 2.Department of MathematicsKyushu UniversityFukuokaJapan

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