Equigenerated ideals of analytic deviation one
Abstract
The overall goal is to approach the Cohen--Macaulay property of the special fiber $\mathcal{F}(I)$ of an equigenerated homogeneous ideal $I$ 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 $\mathcal{F}(I)$. A degree of success is obtained in the case where $I$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.07355
- arXiv:
- arXiv:2009.07355
- Bibcode:
- 2020arXiv200907355R
- Keywords:
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- Mathematics - Commutative Algebra