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On b-functions and algebraic local cohomology classes attached to hypersurfaces with line singularities. (English) Zbl 1327.32044

Summary: Algebraic local cohomology classes attached to Lê cycles of isolated line singularities are considered. A simple method that uses algebraic local cohomology classes to guess the microlocal b-functions associated with line singularities is described. The correctness of the method is shown by using the index theorem of regular singular ordinary differential equations and the notion of vertical monodromy on the stratum of singular locus of a line singularity.

MSC:

32S65 Singularities of holomorphic vector fields and foliations
32S05 Local complex singularities
32C38 Sheaves of differential operators and their modules, \(D\)-modules

Biographic References:

Aoki, Takashi
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