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An Example in Complete Intersections and an Erratum

2017/01/31 by Mandal, Satya
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.00087

Abstract

This is essentially an erratum, with some example to indicate inconsistencies. Suppose A=k[X1, X2, …, Xn] is a polynomial ring over a field k. The Complete Intersection conjecture states that, for any ideal I in A, μ(I)=μ(I/I2), where μ denotes the minimal number of generators. When k is an infinite field, with 1/2∈ k, a proof of this conjecture was claimed recently, which was a consequence of a stronger claim. A counter example of this stronger claim surfaced recently. This note discusses such examples and attempts to provide some clarity to the inconsistencies in the literature.

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