Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four

Details Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four

2011-07-04

arxiv.org/abs/1107.0563v1

Mathematics

Commutative Algebra

22 pages, to appear in Communications in Algebra

Scientific paper

Let $I$ be a squarefree monomial ideal of a polynomial ring $S$. In this
paper, we prove that the arithmetical rank of $I$ is equal to the projective
dimension of $S/I$ when one of the following conditions is satisfied: (1) $\mu
(I) \leq 5$; (2) $\arithdeg I \leq 4$.

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