D-MODULES OVER THE ARRANGEMENTS OF HYPERPLANES

Let A be a collection of hyperplanes in complex affine space, D-X be a sheaf of differential operators over corresponding stratified space X and C-A be a category of all holonomic D-X modules with regular singu larities flat along the stata. We describe in terms of quivers with re lations the full, closed under extensions subcategory C-A(0) subset of C-A generated by delta-functions over the strata. We describe also qu ite explicitely both functors establishing equivalence of C-A(0) with a category of quivers. As a consequence we obtain a description of all D-X-modules from C-A(0) in terms of generators and relations. Applica tion of this results to direct images of local systems over the comple ment to the arrangement of hyperplanes produces a natural complex whic h coincides with Orlik-Solomon complex in the case of trivial monodrom ies.