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"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"--

Geometry, Algebraic. --- Hodge theory. --- Surfaces, Algebraic. --- Géométrie algébrique. --- Hodge, Théorie de. --- Surfaces algébriques. --- Hodge theory --- Geometry, Algebraic