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arXiv · 2508.17748

Q-factoriality and Hodge-Du Bois theory

Sung Gi Park·Mihnea Popa
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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.

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Sung Gi Park, Mihnea Popa. 2025-08-25. Q-factoriality and Hodge-Du Bois theory. https://arxiv.org/abs/2508.17748

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