Perfect modules with Betti numbers $(2,6,5,1)$
Commutative Algebra
2020-03-17 v1
Abstract
In 2018 Celikbas, Laxmi, Kra\'skiewicz, and Weyman exhibited an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. All previously known perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two had been found by Brown in 1987. Brown's ideals all have non-trivial multiplication on the Tor algebra. We prove that all of the ideals of Brown are obtained from the ideals of Celikbas, Laxmi, Kra\'skiewicz, and Weyman by (non-homogeneous) specialization. We also prove that both families of ideals, when built using power series variables over a field, define rigid algebras in the sense of Lichtenbaum and Schlessinger.
Cite
@article{arxiv.2003.06540,
title = {Perfect modules with Betti numbers $(2,6,5,1)$},
author = {Andrew R. Kustin},
journal= {arXiv preprint arXiv:2003.06540},
year = {2020}
}