Arithmetical rank of squarefree monomial ideals of small arithmetic degree

DOI10.1007/s10801-008-0142-3zbMath1244.13016OpenAlexW1969699519MaRDI QIDQ1016572

Kyouko Kimura, Naoki Terai, Ken-ichi Yoshida

Publication date: 6 May 2009

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10801-008-0142-3

zbMATH Keywords

regularityAlexander dualityalmost complete intersectionarithmetical rankarithmetic degreeinitial degree

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55)

Related Items (17)

Lattices and hypergraphs associated to square-free monomial ideals ⋮ Hypergraphs with high projective dimension and 1-dimensional hypergraphs ⋮ On the dimension of dual modules of local cohomology and the Serre's condition for the unmixed Stanley-Reisner ideals of small height ⋮ Licci squarefree monomial ideals generated in degree two or with deviation two ⋮ Arithmetical rank of Gorenstein squarefree monomial ideals of height three ⋮ Arithmetical Rank of Squarefree Monomial Ideals Generated by Five Elements or with Arithmetic Degree Four ⋮ Regularity, depth and arithmetic rank of bipartite edge ideals ⋮ HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS ⋮ Schmitt-Vogel type lemma for reductions ⋮ Arithmetical Ranks of Stanley–Reisner Ideals of Simplicial Complexes with a Cone ⋮ Projective Dimension of String and Cycle Hypergraphs ⋮ Unmixedness and arithmetic properties of matroidal ideals ⋮ Arithmetical rank of a squarefree monomial ideal whose Alexander dual is of deviation two ⋮ Lyubeznik resolutions and the arithmetical rank of monomial ideals ⋮ Cleanness of Cohen-Macaulay monomial ideal generated by at most five elements ⋮ Binomial arithmetical rank of edge ideals of forests ⋮ Projective dimension of hypergraphs

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• On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals
• On the number of equations defining certain varieties
• An étale analog of the Goresky-MacPherson formula for subspace arrangements
• Arithmetical Ranks of Stanley–Reisner Ideals Via Linear Algebra
• On the Arithmetical Rank of the Edge Ideals of Forests
• On set-theoretic intersections

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