Methods for computing b-functions associated with μ-constant deformations – Case of inner modality 2 –

01/05/2021

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by   Katsusuke Nabeshima, et al.

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New methods for computing parametric local b-functions are introduced for μ-constant deformations of semi-weighted homogeneous singularities. The keys of the methods are comprehensive Gröbner systems in Poincaré-Birkhoff-Witt algebra and holonomic 𝒟-modules. It is shown that the use of semi-weighted homogeneity reduces the computational complexity of b-functions associated with μ-constant deformations. In the case of inner modality 2, local b-functions associated with μ-constant deformations are obtained by the resulting method and given the list of parametric local b-functions.