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Computing Tjurina stratifications of \(\mu \)-constant deformations via parametric local cohomology systems

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Abstract

Algebraic local cohomology classes associated with parametric semi-quasihomogeneous hypersurface isolated singularities are considered in the context of symbolic computation. The motivations for this paper are computer calculations of complete lists of Tjurina numbers of semi-quasihomogeneous polynomials with isolated singularity. A new algorithm, that utilizes parametric local cohomology systems, is proposed to compute Tjurina stratifications associated with \(\mu \)-constant deformations of weighted homogeneous isolated singularities. The resulting algorithm gives in particular a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology systems. An efficient algorithm of computing parametric standard bases of relevant ideals is also given as an application of parametric local cohomology systems.

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Acknowledgments

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

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Authors and Affiliations

  1. Graduate School of Science and Technology, Tokushima University, 1-1, Minamijosanjima, Tokushima, Japan

    Katsusuke Nabeshima

  2. Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1, Tennoudai, Tsukuba, 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 paper is a full version of the extended abstract [12].

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Nabeshima, K., Tajima, S. Computing Tjurina stratifications of \(\mu \)-constant deformations via parametric local cohomology systems. AAECC 27, 451–467 (2016). https://doi.org/10.1007/s00200-016-0289-4

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  • DOI: https://doi.org/10.1007/s00200-016-0289-4

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