Stability of depths of symbolic powers of Stanley-Reisner ideals

DOI10.1016/j.jalgebra.2016.10.036zbMath1358.13020OpenAlexW2555993371MaRDI QIDQ502724

Tran Nam Trung, Kyouko Kimura, Naoki Terai, Lê Tuân Hoa

Publication date: 6 January 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2016.10.036

zbMATH Keywords

depthsymbolic powerStanley-Reisner idealcover ideal

Mathematics Subject Classification ID

Applications of graph theory (05C90) Local cohomology and commutative rings (13D45) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

Related Items

Limit behavior of the rational powers of monomial ideals ⋮ Depth Functions and Symbolic Depth Functions of Homogeneous Ideals ⋮ ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS ⋮ Depth and Stanley depth of symbolic powers of cover ideals of graphs ⋮ Regularity of powers of cover ideals of bipartite graphs ⋮ Lower bounds for the depth of symbolic powers of edge ideals of graphs ⋮ Stability of depth and Cohen-Macaulayness of integral closures of powers of monomial ideals ⋮ Epsilon multiplicity and analytic spread of filtrations ⋮ Depth of Powers of Squarefree Monomial Ideals (Research) ⋮ Minimal depth of monomial ideals via associated radical ideals ⋮ SYMBOLIC ANALYTIC SPREAD: UPPER BOUNDS AND APPLICATIONS ⋮ Depth and regularity of monomial ideals via polarization and combinatorial optimization ⋮ Regularity of powers of cover ideals of unimodular hypergraphs ⋮ Stability of depth functions of cover ideals of balanced hypergraphs ⋮ Regularity and Koszul property of symbolic powers of monomial ideals ⋮ Symbolic powers of sums of ideals ⋮ Stability of depth and Stanley depth of symbolic powers of squarefree monomial ideals ⋮ Depth functions of symbolic powers of homogeneous ideals

Cites Work

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• Bounds on the regularity and projective dimension of ideals associated to graphs
• Persistence and stability properties of powers of ideals
• On local cohomology of a tetrahedral curve
• Koszulness, Krull dimension, and other properties of graph-related algebras
• Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals
• Symbolic powers of monomial ideals and vertex cover algebras
• The stable set of associated prime ideals of a polymatroidal ideal
• Replication in critical graphs and the persistence of monomial ideals
• The depth of powers of an ideal
• On the radical of a monomial ideal
• The asymptotic nature of the analytic spread
• Symbolic powers and matroids
• Depths of Powers of the Edge Ideal of a Tree
• Stability of depths of powers of edge ideals