Du Bois complex and extension theorems for holomorphic forms

Sung Gi Park, Harvard
Fine Hall 322

In this talk, I will discuss the extendibility of holomorphic forms from the smooth locus of a variety to forms on a resolution of singularities. In particular, I will present a new result that unifies and generalizes the previous extension theorems of Flenner, Greb-Kebekus-Kovács-Peternell, and Kebekus-Schnell. To illustrate the simplest example of new cases, if a variety has log canonical singularities in codimension two, then 1-forms extend. This is based on a Hodge module theoretic interpretation of Du Bois complexes, offering a methodology that can be used to obtain a new proof of the Theorem of Kollár-Kovács that log canonical singularities are Du Bois.