Restriction, subadditivity, and semicontinuity theorems for Hodge ideals

TL;DR

This paper investigates the properties of Hodge ideals, focusing on their behavior under restriction, addition, and morphisms, using mixed Hodge modules and the V-filtration as key tools.

Contribution

It provides new restriction, subadditivity, and semicontinuity theorems for Hodge ideals, enhancing understanding of their behavior in algebraic geometry.

Findings

Hodge ideals behave predictably under restriction to hypersurfaces.

Subadditivity properties of Hodge ideals are established.

Semicontinuity results for Hodge ideals are proven.

Abstract

We prove results concerning the behavior of Hodge ideals under restriction to hypersurfaces or fibers of morphisms, and addition. The main tool is the description of restriction functors for mixed Hodge modules by means of the $V$-filtration.