Hodge ideals
arXiv:1605.08088
Abstract
We use methods from birational geometry to study M. Saito's 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.
85 pages; v2: minor expository improvements; fixed the statement of Theorem 31.1, and some consequences; moved one result to a new article; v.3: reference added and small expository changes; v.4: new references added, a few further corrections and expository improvements