Equigenerated ideals of analytic deviation one
Abstract
The overall goal is to approach the Cohen--Macaulay property of the special fiber 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, analytical tightness and analytical adjustment, in order to approach the Cohen--Macaulayness of 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.
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