An algorithm for Hodge ideals

TL;DR

This paper introduces an algorithm to compute Hodge ideals for $Q$-divisors, leveraging the $V$-filtration, which also enables calculation of multiplier ideals and jumping numbers for effective divisors.

Contribution

The paper develops a novel algorithm that computes Hodge ideals and related invariants using the $V$-filtration, extending computational tools in algebraic geometry.

Findings

Algorithm successfully computes Hodge ideals for any reduced effective divisor.

Enables calculation of multiplier ideals and jumping numbers.

Provides a new computational approach in the study of divisors.

Abstract

We present an algorithm to compute the Hodge ideals of $\mathbb{Q}$-divisors associated to any reduced effective divisor $D$. The computation of the Hodge ideals is based on an algorithm to compute parts of the $V$-filtration of Malgrange and Kashiwara on $\iota_{+}\mathscr{O}_X(*D)$ and the characterization of the Hodge ideals in terms of this $V$-filtration. In particular, this gives a new algorithm to compute the multiplier ideals and the jumping numbers of any effective divisor.