Hodge ideals

2016/05/25 by Mircea Mustaţă, Mustata, Mircea, Mihnea Popa +1 · 3 citations
Mathematics · Engineering · #Algebraic Geometry and Number Theory #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/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.

Cited by

• Singularities of base loci on abelian varieties
• Multiplier modules, V-filtrations and Bernstein-Sato polynomials on singular ambient varieties
• Inversion of adjunction for higher rational singularities

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