Abstract
AbstractWe study the Hodge and weight filtrations on the localization along a hypersurface, using methods from birational geometry and theV-filtration induced by a local defining equation. These filtrations give rise to ideal sheaves called weighted Hodge ideals, which include the adjoint ideal and a multiplier ideal. We analyze their local and global properties, from which we deduce applications related to singularities of hypersurfaces of smooth varieties.
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