Q-factoriality and Hodge-Du Bois theory
Algebraic Geometry
2025-08-26 v1
Abstract
We prove Hodge-theoretic formulas for the -factoriality defect of a normal projective variety, and for the local analytic -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.
Cite
@article{arxiv.2508.17748,
title = {Q-factoriality and Hodge-Du Bois theory},
author = {Sung Gi Park and Mihnea Popa},
journal= {arXiv preprint arXiv:2508.17748},
year = {2025}
}
Comments
34 pages. Second part of a two-paper replacement of arXiv:2410.15638, on the (local, analytic) Q-factoriality defect via Hodge theory