Abstract
An effective method for computing parametric standard bases of Jacobian ideals is introduced for semi-weighted homogeneous isolated hypersurface singularities. The advantage is that the proposed method is algorithmically simple. The main ideas of the method are the use of a negative weighted term ordering and coefficients in a field of rational functions. The correctness of the method is proved by utilizing algebraic local cohomology classes associated to semi-weighted homogeneous singularities.
This work has been partly supported by JSPS Grant-in-Aid for Scientific Research (C) (18K03214).
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Notes
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The Singular implementation of CSS is in the author’s web-page or the following URL. https://www-math.ias.tokushima-u.ac.jp/~nabesima/softwares.html.
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Nabeshima, K. (2020). Computing Parametric Standard Bases for Semi-weighted Homogeneous Isolated Hypersurface Singularities. 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_26
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