Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities
-- Christian Schnell, October 26, 2018

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Suppose we have an algebraic (or holomorphic) differential form, defined on the smooth locus of an algebraic variety (or analytic space). Under what conditions does it extend to an algebraic (or holomorphic) differential form on a resolution of singularities? In 2011, Greb, Kebekus, Kovacs, and Peternell proved that such an extension always exists on algebraic varieties with klt singularities. I will explain how to generalize their result to a much larger class of singular spaces, with the help of Hodge modules and the decomposition theorem. This is joint work with Kebekus.