Hilbert depth of powers of the maximal ideal

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.

AmS-LaTeX, 13 pages; fixed a gap in Lemma 3.5 pointed out by Jiayuan Lin