Lyubeznik numbers of projective schemes

Let X be a projective scheme over a field k and let A be the local ring at the vertex of the affine cone of X under some embedding . We prove that, when char(k)>0, the Lyubeznik numbers λi,j(A) are intrinsic numerical invariants of X, i.e., λi,j(A) depend only on X, but not on the embedding.