METHODS FOR COMPUTING b-FUNCTIONS ASSOCIATED WITH µ-CONSTANT DEFORMATIONS: CASE OF INNER MODALITY TWO

Abstract

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 two, local b-functions associated with µ-constant deformations are obtained by the resulting method and given the list of parametric local b-functions.