CSSg method for several genericities of parametric systems

摘要

Abstract 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 κdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$kappa$$end{document}-invariants and local Euler obstructions for parametric cases are given. Furthermore, κdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$kappa$$end{document}-invariants associated to μdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mu$$end{document}-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.