An algorithm to compute the Hilbert depth

TL;DR

This paper introduces an algorithm for calculating the Hilbert depth of graded modules, addressing a question about how Hilbert depth behaves under direct sums, with implications for algebraic module analysis.

Contribution

The paper presents a novel algorithm for computing Hilbert depth, expanding understanding of its properties, especially in relation to direct sums of modules.

Findings

The algorithm effectively computes Hilbert depth for graded modules.

Hilbert depth of a direct sum can exceed that of individual summands.

Addresses Herzog's question on Hilbert depth behavior.

Abstract

We present an algorithm which computes the Hilbert depth of a graded module based on a theorem of Uliczka. Connected to a Herzog's question we see that the Hilbert depth of a direct sum of modules can be strictly bigger than the Hilbert depth of all the summands.