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.
Similar content being viewed by others
References
Blickle M., Mustaţǎ M., Smith K.E.: Discreteness and rationality of F-thresholds. Michigan Math. J. 57, 43–61 (2008)
de Fernex, T., Mustaţǎ, M.: Limits of log canonical thresholds, arXiv:0710.4978. Ann. Sci. Ecole Norm. Sup. (to appear)
Eisenbud D., Strumfels B.: On binomial ideals. Duke Math. J. 84, 1–45 (1996)
Hara N., Yoshida K.: A generalization of tight closure and multiplier ideals. Trans. Am. Math. Soc. 355, 3143–3174 (2003)
Hironaka H.: Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. Math. (2) 79, 109–203 (1964)
Hironaka H.: Resolution of singularities of an algebraic variety over a field of characteristic zero I, II. Ann. Math. (2) 79, 205–326 (1964)
Howald J.: Multiplier ideals of monomial ideals. Trans. Am. Math. Soc. 353, 2665–2671 (2001)
Howald, J.: Multiplier ideals of sufficiently general polynomials, arXiv:math. AG/0303203 (2003, preprint)
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)
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)
Röhrl, N.: Binomial regular sequences and S-matrices, Diplomarbeit, Universität Regensburg, available at http://www.iadm.uni-stuttgart.de/LstAnaMPhy/Roehrl/ (1998)
Shibuta, T.: An algorithm for computing multiplier ideals, arXiv:0807.4302 (2008, preprint)
Takagi S.: Formulas for multiplier ideals on singular varieties. Am. J. Math. 128, 1345–1362 (2006)
Takagi S., Watanabe K.-i.: On F-pure thresholds. J. Algebra 282(1), 278–297 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Toshiyuki Katsura on the occasion of his sixtieth birthday
Rights 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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-009-0270-7