A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals

Katsusuke Nabeshima, Shinichi Tajima

Research output: Contribution to journalArticlepeer-review

Abstract

A new algorithm is introduced for computing logarithmic vector fields along a hypersurface with an isolated singularity. The key ideas of the algorithm are computing an ideal quotient in a polynomial ring and the use of algebraic local cohomology. The use of these ideas allows us to compute a module, over a local ring, of germs logarithmic vector fields. The resulting algorithms are much faster than our previous algorithms in computation speed. As the applications, an effective method of computing Bruce-Roberts Milnor and Tjurina ideals (or numbers) is also introduced.

Original languageEnglish
Pages (from-to)190-208
Number of pages19
JournalJournal of Symbolic Computation
Volume107
DOIs
Publication statusPublished - 1 Nov 2021

Keywords

  • Gröbner bases
  • Isolated singularities
  • Local cohomology
  • Logarithmic vector fields

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