A new framework for treating several genericities of parametric systems is proposed. A computational method (CSSg) of comprehensive standard system over a field of rational functions is introduced as a key tool. As application to singularity theory, algorithms of computing parameter dependency of κ-invariants and local Euler obstructions for parametric cases are given. Furthermore, κ-invariants associated to μ-constant deformations are given by using the resulting algorithm. As another application, an algorithm of computing Hilbert–Samuel multiplicities of parametric ideals is provided to show the versatility of the proposed framework.
|Journal||Japan Journal of Industrial and Applied Mathematics|
|Publication status||Accepted/In press - 2022|
- Comprehensive standard system
- Deformation of an isolated hypersurface singularity
- Hilbert–Samuel multiplicity
- Local Euler obstruction