Holonomic <i>D</i>-Modules Associated with a Simple Line Singularity and the Vertical Monodromy

Abstract

Holonomic D-modules associated with certain kind of non-isolated hypersurface singularities, introduced by T. de Jong, are considered. Structures of these holonomic D-modules such as characteristic variety, monodromy are explicitly determined. The key of our approach is the use of the notion of algebraic local cohomology. An application to Betti numbers of local Milnor fibers is also discussed.