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Computing Logarithmic Vector Fields Along an ICIS Germ via Matlis Duality

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Computer Algebra in Scientific Computing (CASC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12291))

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Abstract

Logarithmic vector fields along an isolated complete intersection singularity (ICIS) are considered in the context of computational complex analysis. Based on the theory of local polar varieties, an effective method is introduced for computing a set of generators, over a local ring, of the modules of germs of logarithmic vector fields. Underlying ideas of our approach are the use of a parametric version of the concept of local cohomology and the Matlis duality. The algorithms are designed to output a set of representatives of logarithmic vector fields which is suitable to study their complex analytic properties. Some examples are given to illustrate the resulting algorithms.

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

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Author information

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 Information Science, Kyushu Sangyo University, 2-3-1, Shokadai, Higashiku, Fukuoka, Japan

    Takafumi Shibuta

  3. Graduate School of Technology, Industrial and Social Sciences, Tokushima University, 2-1, Minamijosanjima-cho, Tokushima, Japan

    Katsusuke Nabeshima

Authors
  1. Shinichi Tajima
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  2. Takafumi Shibuta
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  3. Katsusuke Nabeshima
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Correspondence to Katsusuke Nabeshima .

Editor information

Editors and Affiliations

  1. University of Lille, Villeneuve d’Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Tajima, S., Shibuta, T., Nabeshima, K. (2020). Computing Logarithmic Vector Fields Along an ICIS Germ via Matlis Duality. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2020. Lecture Notes in Computer Science(), vol 12291. Springer, Cham. https://doi.org/10.1007/978-3-030-60026-6_32

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  • DOI: https://doi.org/10.1007/978-3-030-60026-6_32

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