2023/11/26 by Sung Gi Park, Park, Sung Gi · 3 citations
Mathematics · #14B05 #14E30 #14F10 #32S35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2311.15159
openalex publication_date 2023/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a characterization of the Du Bois complex of a reduced pair (X,Z) when X\smallsetminus Z has rational singularities. As an application, when X has normal Du Bois singularities and Z is the locus of non-rational singularities of X, holomorphic p-forms on the smooth locus of X extend regularly to forms on a resolution of singularities for p\lecodimX Z-1, and to forms with log poles over Z for p\gecodimX Z. If X is not necessarily Du Bois, then p-forms extend regularly for p\lecodimX Z-2. This is a generalization of the theorems of Flenner, Greb-Kebekus-Kovács-Peternell, and Kebekus-Schnell on extending holomorphic (log) forms. A by-product of our methods is a new proof of the theorem of Kollár-Kovács that log canonical singularities are Du Bois. We also show that the Proj of the log canonical ring of a log canonical pair is Du Bois if this ring is finitely generated. The proofs are based on Saito's theory of mixed Hodge modules.