TL;DR
This paper investigates Hodge ideals, a sequence of ideal sheaves derived from the Hodge filtration on hypersurface localizations, exploring their properties and applications to singularity and Hodge theory analysis.
Contribution
It introduces a new framework connecting Hodge filtration and birational geometry to study hypersurface singularities and their Hodge-theoretic properties.
Findings
Hodge ideals generalize multiplier ideals.
They provide new insights into hypersurface singularities.
Applications include characterizing singularities and Hodge structures.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Commutative Algebra and Its Applications