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On the projective dimension and the unmixed part of three cubics

Published Web Location

https://doi.org/10.1016/j.jalgebra.2006.11.018
Abstract

Let R be a polynomial ring over a field in an unspecified number of variables. We prove that if J in R is an ideal generated by three cubic forms, and the unmixed part of J contains a quadric, then the projective dimension of R/J is at most 4. To this end, we show that if K in R is a three-generated ideal of height two and L in R an ideal linked to the unmixed part of K, then the projective dimension of R/K is bounded above by the projective dimension of R/L plus one. (c) 2006 Elsevier Inc. All rights reserved.

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