Tajima, Shinichi On b-functions and algebraic local cohomology classes attached to hypersurfaces with line singularities. (English) Zbl 1327.32044 RIMS Kôkyûroku Bessatsu B52, 175-191 (2014). 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. Cited in 1 Document MSC: 32S65 Singularities of holomorphic vector fields and foliations 32S05 Local complex singularities 32C38 Sheaves of differential operators and their modules, \(D\)-modules Keywords:isolated line singularities; b-functions; local cohomology; Lê cycles; holonomic \(\mathcal D\)-modules Biographic References: Aoki, Takashi PDFBibTeX XMLCite \textit{S. Tajima}, RIMS Kôkyûroku Bessatsu B52, 175--191 (2014; Zbl 1327.32044)