Hilbert depth of powers of the maximal ideal

TL;DR

This paper computes the Hilbert depth of powers of the maximal ideal in a polynomial ring, providing explicit values and insights into their algebraic structure.

Contribution

It offers a precise calculation of the Hilbert depths for powers of the maximal ideal, advancing understanding of their algebraic properties.

Findings

Explicit Hilbert depth values for powers of the maximal ideal

Enhanced understanding of the algebraic structure of these modules

Potential applications in commutative algebra and algebraic geometry

Abstract

The Hilbert depth of a module M is the maximum depth that occurs among all modules with the same Hilbert function as M. In this note we compute the Hilbert depths of the powers of the irrelevant maximal ideal in a standard graded polynomial ring.