English

Equigenerated ideals of analytic deviation one

Commutative Algebra 2020-09-17 v1

Abstract

The overall goal is to approach the Cohen--Macaulay property of the special fiber F(I)\mathcal{F}(I) of an equigenerated homogeneous ideal II in a standard graded ring over an infinite field. When the ground ring is assumed to be local, the subject has been extensively looked at. Here, with a focus on the graded situation, one introduces two technical conditions, called respectively, {\em analytical tightness} and {\em analytical adjustment}, in order to approach the Cohen--Macaulayness of F(I)\mathcal{F}(I). A degree of success is obtained in the case where II in addition has analytic deviation one, a situation looked at by several authors, being essentially the only interesting one in dimension three. Naturally, the paper has some applications in this case.

Keywords

Cite

@article{arxiv.2009.07355,
  title  = {Equigenerated ideals of analytic deviation one},
  author = {Zaqueu Ramos and Aron Simis},
  journal= {arXiv preprint arXiv:2009.07355},
  year   = {2020}
}
R2 v1 2026-06-23T18:34:16.089Z