Algorithms for Bernstein-Sato polynomials and multiplier ideals

Christine Berkesch, Anton Leykin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

The Bernstein-Sato polynomial (or global b-function) is an important invariant in singularity theory, which can be computed using symbolic methods in the theory of D-modules. After providing a survey of known algorithms for computing the global b-function, we develop a new method to compute the local b-function for a single polynomial. We then develop algorithms that compute generalized Bernstein-Sato polynomials of Budur-MustaÇâ-Saito and Shibuta for an arbitrary polynomial ideal. These lead to computations of log canonical thresholds, jumping coefficients, and multiplier ideals. Our algorithm for multiplier ideals simplifies that of Shibuta and shares a common subroutine with our local b-function algorithm. The algorithms we present have been implemented in the D-modules package of the computer algebra system Macaulay2.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
PublisherAssociation for Computing Machinery (ACM)
Pages99-106
Number of pages8
ISBN (Print)9781450301503
DOIs
StatePublished - 2010
Event2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 - Munich, Germany
Duration: Jul 25 2010Jul 28 2010

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Other

Other2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
CountryGermany
CityMunich
Period7/25/107/28/10

Keywords

  • Bernstein-Sato polynomial
  • D-modules
  • Jumping coefficients
  • Log-canonical threshold
  • Multiplier ideals
  • V-filtration

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    Berkesch, C., & Leykin, A. (2010). Algorithms for Bernstein-Sato polynomials and multiplier ideals. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 (pp. 99-106). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). Association for Computing Machinery (ACM). https://doi.org/10.1145/1837934.1837958