Du Bois complex and extension of forms beyond rational singularities
Sung Gi Park

TL;DR
This paper characterizes the Du Bois complex for pairs with rational singularities, extends holomorphic forms over singularities, and provides new proofs and generalizations of existing theorems using mixed Hodge modules.
Contribution
It offers a new characterization of the Du Bois complex for pairs with rational singularities and generalizes form extension theorems beyond Du Bois singularities.
Findings
Holomorphic forms extend over singularities with bounds depending on codimension.
A new proof that log canonical singularities are Du Bois.
Proves the Du Bois property for the Proj of finitely generated log canonical rings.
Abstract
We establish a characterization of the Du Bois complex of a reduced pair when has rational singularities. As an application, when has normal Du Bois singularities and is the locus of non-rational singularities of , holomorphic -forms on the smooth locus of extend regularly to forms on a resolution of singularities for , and to forms with log poles over for . If is not necessarily Du Bois, then -forms extend regularly for . This is a generalization of the theorems of Flenner, Greb-Kebekus-Kov\'acs-Peternell, and Kebekus-Schnell on extending holomorphic (log) forms. A by-product of our methods is a new proof of the theorem of Koll\'ar-Kov\'acs that log canonical singularities are Du Bois. We also show that the Proj of the log canonical ring of a log…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry
