Hodge Ideals

The authors use methods from birational geometry to study the Hodge filtration on the localization along a hypersurface.

This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal.

They analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.