Depth functions of powers of homogeneous ideals

Abstract

We settle a conjecture of Herzog and Hibi, which states that the function depth $S/Q^n$, $n\ge 1$, where $Q$ is a homogeneous ideal in a polynomial ring $S$, can be any convergent numerical function. We also give a positive answer to a long-standing open question of Ratliff on the associated primes of powers of ideals.

9 pages. This paper is split from the first version of the paper "Symbolic powers of sums of ideals", arXiv:1702.01766, due to a recommendation of its referee

References in corpus (2)

• Symbolic powers of sums of ideals
• Nonincreasing depth functions of monomial ideals