Geodesic
Arithmetical rank of squarefree monomial ideals of small arithmetic degree
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 389-404.

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Summary: 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).
Keywords: keywords arithmetical rank, almost complete intersection, Alexander duality, regularity, arithmetic degree, initial degree 
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     title = {Arithmetical rank of squarefree monomial ideals of small arithmetic degree},
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Kimura, Kyouko; Terai, Naoki; Yoshida, Ken-ichi. Arithmetical rank of squarefree monomial ideals of small arithmetic degree. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 3, pp. 389-404. http://geodesic.mathdoc.fr/item/JAC_2009__29_3_a0/