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An Implementation of the Lê–Teissier Method for Computing Local Euler Obstructions

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Abstract

Local Euler obstruction of a hypersurface with possibly positive dimensional singularities, a constructible function on the hypersurface, is considered in the context of symbolic computation. It is shown that the method due to Lê and Teissier (Ann Math 114:457–491, 1981) that requires genericity conditions for computing local Euler obstructions can be realized as an algorithm in a deterministic way. The key ideas of the proposed algorithm are the use of comprehensive Gröbner systems and of parametric local cohomology systems.

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

    Katsusuke Nabeshima

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

Additional information

This work has been partly supported by JSPS Grant-in-Aid for Scientific Research (Nos. 15KT0102, 15K04891) and JSPS Grant-in-Aid for Young Scientist (B) (No. 15K17513).

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Tajima, S., Nabeshima, K. An Implementation of the Lê–Teissier Method for Computing Local Euler Obstructions. Math.Comput.Sci. 13, 273–280 (2019). https://doi.org/10.1007/s11786-018-0366-0

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  • DOI: https://doi.org/10.1007/s11786-018-0366-0

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