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Partial Cohomologically Complete Intersections via Hodge Theory
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
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