Lyubeznik numbers for nonsingular projective varieties

Abstract

In this paper, we determine completely the Lyubeznik numbers ${\lambda }_{i,j}(A)$ 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.

7 pages; preprint version; final version to appear in Bulletin of the London Mathematical Society

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