Comprehensive Gröbner systems in PBW algebras, Bernstein–Sato ideals and holonomic D-modules. (November 2018) - Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi
Abstract: A computation method of comprehensive Gröbner systems is introduced in Poincaré–Birkhoff–Witt (PBW) algebras and applications to Bernstein–Sato ideals, holonomic D -modules for parametric cases are considered. The proposed method provides in particular holonomic D -modules associated with primary components of Bernstein–Sato ideals. Furthermore, with our implementation, effective methods are illustrated for computing b -functions of μ -constant deformations of hypersurface isolated singularities by utilizing holonomic D -modules. High versatility of the proposed method is also illustrated by several examples.