Minimal quasi-complete intersection ideals
Abstract
A quasi-complete intersection (q.c.i.) ideal of a local ring is an ideal with "free exterior Koszul homology"; the definition can also be understood in terms of vanishing of Andr\'e-Quillen homology functors. Principal q.c.i. ideals are well understood, but few constructions are known to produce q.c.i. ideals of grade zero that are not principal. This paper examines the structure of q.c.i. ideals. We exhibit conditions on a ring which guarantee that every q.c.i. ideal of is principal. On the other hand, we give an example of a minimal q.c.i. deal which does not contain any principal q.c.i. ideals and is not embedded, in the sense that no faithfully flat extension of can be written as a quotient of complete intersection ideals. We also describe a generic situation in which the maximal ideal of is an embedded q.c.i. ideal that does not contain any principal q.c.i. ideals.
Cite
@article{arxiv.1309.1186,
title = {Minimal quasi-complete intersection ideals},
author = {Andrew R. Kustin and Liana M. Şega and Adela Vraciu},
journal= {arXiv preprint arXiv:1309.1186},
year = {2015}
}
Comments
This version contains an appendix, which describes the Macaulay2 commands that can be used to verify the proof of Lemma 4.2