Q-factoriality and Hodge-Du Bois theory

2025/08/25 by Park, Sung Gi, Popa, Mihnea · 2 citations
#14B05 #14C30 #14F10 #32S35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17748

Abstract

We prove Hodge-theoretic formulas for the ℚ-factoriality defect of a normal projective variety, and for the local analytic 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.

Citations

• Hodge symmetry and Lefschetz theorems for singular varieties
• Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups
• Du Bois complex and extension of forms beyond rational singularities
• Higher Du Bois and higher rational singularities
• Deformations of log terminal and semi log canonical singularities
• Deformations of some local Calabi-Yau manifolds
• Factorial threefold hypersurfaces
• Mixed Hodge Complexes on Algebraic Varieties
• A Lefschetz (1,1) Theorem for normal projective complex varieties
• On the extension problem of pluricanonical forms
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities

Cited by

• Defect of projective hypersurfaces with isolated singularities
• Factoriality of normal projective varieties

Related

• Factoriality of normal projective varieties
• Degeneration of families of projective hypersurfaces and Hodge conjecture
• Notes on the Hodge Conjecture for Fermat Varieties
• A Conditional Reduction of the Rational Hodge Conjecture for Threefolds and Deformation-Theoretic Verifications in Several Families
• Hodge conjecture for projective hypersurface