Depth functions of powers of homogeneous ideals

Huy Tai Ha; Hop Dang Nguyen; Ngo Viet Trung; Tran Nam Trung

doi:10.1090/proc/15083

Depth functions of powers of homogeneous ideals

Commutative Algebra 2021-10-18 v1 Algebraic Geometry

Authors: Huy Tai Ha , Hop Dang Nguyen , Ngo Viet Trung , Tran Nam Trung

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

depth function homogeneous ideal powers of ideals convergent numerical function associated primes

Cite

@article{arxiv.1904.07587,
  title  = {Depth functions of powers of homogeneous ideals},
  author = {Huy Tai Ha and Hop Dang Nguyen and Ngo Viet Trung and Tran Nam Trung},
  journal= {arXiv preprint arXiv:1904.07587},
  year   = {2021}
}

Comments

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

Depth functions of powers of homogeneous ideals

Abstract

Keywords

Cite

Comments

Related papers