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 $X\hookrightarrow\mathbb{P}^n_k$. We prove that, when $\ch(k)>0$, the Lyubeznik numbers $\lambda_{i,j}(A)$ are intrinsic numerical invariants of $X$, i.e., $\lambda_{i,j}(A)$ depend only on $X$, but not on the embedding.Comment: revised version, exposition improved, to appear in Advances in Mathematic