Lyubeznik numbers for nonsingular projective varieties

eko prasetyo wibowo;

In this paper, we determine completely the Lyubeznik numbers λi,j(A) of the local ring A at the vertex of the affine cone over a nonsingular projective variety V, where V is defined over a field of characteristic zero, in terms of the dimensions of the algebraic de Rham cohomology spaces of V . In particular, we prove that these numbers are intrinsic numerical invariants of V , even though a priori their definition depends on an embedding into projective space. This provides supporting evidence for a positive answer to the question of embedding-independence for arbitrary varieties in characteristic zero, which is still open.