Simple D-module components of local cohomology modules

Abstract For a projective variety V ⊂ P k n over a field of characteristic zero, with homogeneous ideal I in A = k [ x 0 , … , x n ] , we consider the local cohomology modules H I i ( A ) . These have a structure of holonomic D -module over A , and we investigate their filtration by simple D -modules. In case V is nonsingular, we can describe completely the simple D -module components of H I i ( A ) for all i , in terms of the Betti numbers of V .