For a projective variety V?Pkn over field of characteristic zero, with homogeneous ideal I in A=k[x0,…,xn], we consider the local cohomology modules HIi(A). These have structure holonomic D-module A, and investigate their filtration by simple D-modules. In case V is nonsingular, can describe completely components HIi(A) for all i, terms Betti numbers V.

All rings in this paper are commutative and Noetherian. If R is a ring and I ⊂ R is an ideal, cd(R, I) denotes the cohomological dimension of I in R, i.e. the largest integer i such that the i-th local cohomology module H i I(M) doesn’t vanish for some R-module M . For the purposes of this introduction R is a complete equicharacteristic regular local d-dimensional ring with a separably closed r...