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CSSg method for several genericities of parametric systems

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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 \(\kappa\)-invariants and local Euler obstructions for parametric cases are given. Furthermore, \(\kappa\)-invariants associated to \(\mu\)-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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Tokyo, Japan

    Katsusuke Nabeshima

  2. Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, Japan

    Shinichi Tajima

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  1. Katsusuke Nabeshima
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  2. Shinichi Tajima
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Correspondence to Katsusuke Nabeshima.

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This work has been partly supported by JSPS Grant-in-Aid for Science Research (C) (18K03320 and 18K03214).

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Nabeshima, K., Tajima, S. CSSg method for several genericities of parametric systems. Japan J. Indust. Appl. Math. 40, 315–337 (2023). https://doi.org/10.1007/s13160-022-00520-3

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  • DOI: https://doi.org/10.1007/s13160-022-00520-3

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