Abstract
In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg?I=reg?I; (c) arithdeg?I=indeg?I+1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in case (c).
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