Differential operators on cones (Q809451)

A linear system of partial differential equations on a complex manifold Y is a module over the ring \({\mathcal D}_ Y\) of holomorphic linear differential operators on Y. A theorem of Kashiwara states that \({\mathcal D}_ Y\)-modules supported on a submanifold Z are the same thing as \({\mathcal D}_ Z\)-modules. Because the analogue of this theorem may fail if Z is singular, Kashiwara has posed the problem of finding an appropriate Z-intrinsic characterization of the category of \({\mathcal D}_ Y\)-modules supported on singular Z. The aim of this paper is to give a partial answer to this question, namely: If Z is a cone, the existence of a spectral sequence for computing \({\mathcal D}_ Z\) is proved and then this result is applied when Y is a Riemann surface of genus greater than one or an Abelian variety.