On b-functions and algebraic local cohomology classes attached to hypersurfaces with line singularities : Dedicated to Professor Takashi Aoki on the occasion of his sixtieth birthday (Exponential Analysis of Differential Equations and Related Topics)

Abstract

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.