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arXiv · 2101.01384

Methods for computing $b$-functions associated with $\mu$-constant deformations -- Case of inner modality 2 --

Katsusuke Nabeshima·Shinichi Tajima
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Abstract

New methods for computing parametric local $b$-functions are introduced for $\mu$-constant deformations of semi-weighted homogeneous singularities. The keys of the methods are comprehensive Gr\"obner systems in Poincar\'e-Birkhoff-Witt algebra and holonomic ${\mathcal D}$-modules. It is shown that the use of semi-weighted homogeneity reduces the computational complexity of $b$-functions associated with $\mu$-constant deformations. In the case of inner modality 2, local $b$-functions associated with $\mu$-constant deformations are obtained by the resulting method and given the list of parametric local $b$-functions.

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Katsusuke Nabeshima, Shinichi Tajima. 2021-01-05. Methods for computing $b$-functions associated with $\mu$-constant deformations -- Case of inner modality 2 --. https://arxiv.org/abs/2101.01384

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