Arithmetical rank of strings and cycles

2014/07/21 by Kyouko Kimura, Kimura, Kyouko, Paolo Mantero +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1407.5571

14 pages, comments welcome

arxiv created 2014/07/21 · arxiv updated 2014/07/22

Abstract

Let R be a polynomial ring over a field K. To a given squarefree monomial ideal I ⊂ R, one can associate a hypergraph H(I). In this article, we prove that the arithmetical rank of I is equal to the projective dimension of R/I when H(I) is a string or a cycle hypergraph.

Related

• Projective dimension of Hypergraphs
• Projective Dimension of String and Cycle Hypergraphs
• Arithmetical rank of squarefree monomial ideals generated by five elements or with arithmetic degree four
• The arithmetical rank of a special class of monomial ideals
• Lattices and Hypergraphs associated to square-free monomial ideals