Lyubeznik numbers of projective schemes

Abstract

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 $X\hookrightarrow {\mathbb{P}}_k^n$. We prove that, when $\mathrm{ch}(k)>0$, 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.

revised version, exposition improved, to appear in Advances in Mathematics