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 language English 190-208 19 Journal of Symbolic Computation 107 https://doi.org/10.1016/j.jsc.2021.03.003 Published - 1 Nov 2021

Keywords

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