Arithmetical rank of squarefree monomial ideals of small arithmetic degree
نویسندگان
چکیده
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).
منابع مشابه
Schmitt–Vogel type lemma for reductions
The lemma given by Schmitt and Vogel is an important tool in the study of the arithmetical rank of squarefree monomial ideals. In this paper, we give a Schmitt–Vogel type lemma for reductions as an analogous result. Mathematics Subject Classification (2010). 13A30.
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