Partial Cohomologically Complete Intersections via Hodge Theory

Abstract

We introduce an invariant $c(X)$ associated to any complex algebraic variety $X$, which for varieties with isolated singularities measures the failure of dual Kodaira-Akizuki-Nakano vanishing. In general, it is characterized by Hodge--Lyubeznik numbers, the depth of Du Bois complexes, and the Hodge filtration on local cohomology modules. We show that this invariant is computable in many examples, such as cones over rational homology manifolds or determinantal varieties.

arXiv commentv1: 45 pages; v2: 40 pages, rewrote introduction, improved exposition throughout, and added Corollary 2.6