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Computing Holonomic D-Modules Associated to a Family of Non-isolated Hypersurface Singularities via Comprehensive Gröbner Systems of PBW Algebra

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Abstract

The reduced b-functions and the relevant holonomic D-modules associated to a family of hypersurfaces with non-isolated singularities are considered in the context of symbolic computation. Based on the theory of comprehensive Gröbner systems, algorithms of computing reduced b-functions and holonomic D-modules for parametric cases are introduced. A strategy for analyzing holonomic D-modules is described. Main ingredients of our approach are comprehensive Gröbner systems on Poincaré–Birkhoff–Witt algebra and local cohomology.

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Authors and Affiliations

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

    Shinichi Tajima

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

    Katsusuke Nabeshima

  3. Faculty of Mathematics and Physics, Kanazawa University, Kakuma-machi, Kanazawa, Japan

    Katsuyoshi Ohara

  4. Department of Mathematics, Josai University, 3-26, Kioicho, Chiyoda-ku, Tokyo, Japan

    Yoko Umeta

Authors
  1. Shinichi Tajima
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  2. Katsusuke Nabeshima
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  3. Katsuyoshi Ohara
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  4. Yoko Umeta
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Correspondence to Shinichi Tajima.

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This work has been partly supported by JSPS Grant-in-Aid for Science Research (C) (18K03320, 18K03214, 20K03637 and 21K03291).

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Tajima, S., Nabeshima, K., Ohara, K. et al. Computing Holonomic D-Modules Associated to a Family of Non-isolated Hypersurface Singularities via Comprehensive Gröbner Systems of PBW Algebra. Math.Comput.Sci. 17, 6 (2023). https://doi.org/10.1007/s11786-022-00553-4

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  • DOI: https://doi.org/10.1007/s11786-022-00553-4

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