Q-factoriality and Hodge-Du Bois theory

Abstract

We prove Hodge-theoretic formulas for the $\mathbb{Q}$-factoriality defect of a normal projective variety, and for the local analytic $\mathbb{Q}$-factoriality defect of an analytic germ of a normal variety. These formulas lead to consequences ranging from a local analytic version of Samuel's conjecture to a characterization of projective rational homology threefolds with rational singularities, or the invariance of Hodge-Du Bois numbers under flops of projective threefolds.

34 pages. Second part of a two-paper replacement of arXiv:2410.15638, on the (local, analytic) Q-factoriality defect via Hodge theory