Skip to main content
Log in

Log canonical thresholds of binomial ideals

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blickle M., Mustaţǎ M., Smith K.E.: Discreteness and rationality of F-thresholds. Michigan Math. J. 57, 43–61 (2008)

    Article  MathSciNet  Google Scholar 

  2. de Fernex, T., Mustaţǎ, M.: Limits of log canonical thresholds, arXiv:0710.4978. Ann. Sci. Ecole Norm. Sup. (to appear)

  3. Eisenbud D., Strumfels B.: On binomial ideals. Duke Math. J. 84, 1–45 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hara N., Yoshida K.: A generalization of tight closure and multiplier ideals. Trans. Am. Math. Soc. 355, 3143–3174 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Howald, J.: Multiplier ideals of sufficiently general polynomials, arXiv:math. AG/0303203 (2003, preprint)

  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)

  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)

  11. Röhrl, N.: Binomial regular sequences and S-matrices, Diplomarbeit, Universität Regensburg, available at http://www.iadm.uni-stuttgart.de/LstAnaMPhy/Roehrl/ (1998)

  12. Shibuta, T.: An algorithm for computing multiplier ideals, arXiv:0807.4302 (2008, preprint)

  13. Takagi S.: Formulas for multiplier ideals on singular varieties. Am. J. Math. 128, 1345–1362 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. Takagi S., Watanabe K.-i.: On F-pure thresholds. J. Algebra 282(1), 278–297 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shunsuke Takagi.

Additional information

Dedicated to Professor Toshiyuki Katsura on the occasion of his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shibuta, T., Takagi, S. Log canonical thresholds of binomial ideals. manuscripta math. 130, 45–61 (2009). https://doi.org/10.1007/s00229-009-0270-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-009-0270-7

Mathematics Subject Classification (2000)

Navigation