Weighted multiplier ideals of reduced divisors

TL;DR

This paper introduces weighted multiplier ideals derived from birational geometry methods to analyze hypersurface singularities, connecting Hodge and weight filtrations with new ideal sheaves and their properties.

Contribution

It defines a sequence of weighted multiplier ideals, establishing the first as the adjoint ideal and linking these to Hodge and multiplier ideals in hypersurface singularity analysis.

Findings

Weighted multiplier ideals form a new sequence of ideal sheaves.

The first weighted multiplier ideal is identified as the adjoint ideal.

Applications to hypersurface singularities are demonstrated.

Abstract

We use methods from birational geometry to study the Hodge and weight filtrations on the localization along a hypersurface. We focus on the lowest piece of the Hodge filtration of the submodules arising from the weight filtration. This leads to a sequence of ideal sheaves called weighted multiplier ideals. The last ideal of this sequence is a multiplier ideal (and a Hodge ideal), and we prove that the first is the adjoint ideal. We also study the local and global properties of weighted multiplier ideals and their applications to singularities of hypersurfaces of smooth varieties.