Hodge Ideals - Mustaţă, Mircea; Popa, Mihnea (Memoirs of the American Mathematical Society, 2019)
We 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. We analyze their local and global properties, and use them for applications related to the singularities and Hodge theory of hypersurfaces and their complements.