Symbolic Powers of Monomial Ideals and Cohen-Macaulay Vertex-Weighted Digraphs

DOI10.1007/978-3-319-96827-8_21zbMath1405.13041arXiv1706.00126OpenAlexW2795763531MaRDI QIDQ4613706

Rafael H. Villarreal, Philippe Gimenez, José Martínez-Bernal, Carlos E. Vivares, Aaron Simis

Publication date: 24 January 2019

Published in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.00126

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items

Equality of ordinary and symbolic powers of edge ideals of weighted oriented graphs ⋮ Toric ideals of weighted oriented graphs ⋮ Comparing symbolic powers of edge ideals of weighted oriented graphs ⋮ Initially regular sequences and depths of ideals ⋮ Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests ⋮ Properties of symbolic powers of edge ideals of weighted oriented graphs ⋮ Barile-Macchia resolutions ⋮ The saturation number of monomial ideals ⋮ Powers of edge ideals of weighted oriented graphs with linear resolutions ⋮ Edge ideals of oriented graphs ⋮ Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs ⋮ Depth and regularity of monomial ideals via polarization and combinatorial optimization ⋮ Betti numbers of weighted oriented graphs ⋮ Algebraic properties of edge ideals of some vertex-weighted oriented \(m\)-partite graphs ⋮ Regularity in weighted oriented graphs ⋮ Projective dimension and regularity of edge ideals of some weighted oriented graphs ⋮ Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals ⋮ On regularity of symbolic Rees algebras and symbolic powers of vertex cover ideals of graphs ⋮ Unmixedness of some weighted oriented graphs ⋮ Algebraic invariants of weighted oriented graphs

Uses Software

• Macaulay2
• Normaliz

Cites Work

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• The Aluffi algebra of the Jacobian of points in projective space: torsion-freeness
• Minimum distance functions of graded ideals and Reed-Muller-type codes
• Bounds on the regularity and projective dimension of ideals associated to graphs
• Integral closure and other operations on monomial ideals
• Regularity and algebraic properties of certain lattice ideals
• The divisor class group of ordinary and symbolic blow-ups
• Progress in commutative algebra 1. Combinatorics and homology
• Symbolic powers of monomial ideals and vertex cover algebras
• A note on Rees algebras and the MFMC property
• On the ideal theory of graphs
• Symbolic powers of edge ideals.
• The Alexander duality functors and local duality with monomial support
• Symbolic powers of ideals
• Cohen-Macaulay graphs
• Depth and regularity of monomial ideals via polarization and combinatorial optimization
• Monomial ideals of weighted oriented graphs
• Projective nested Cartesian codes
• On the radical of a monomial ideal
• On complete monomial ideals
• Embedded associated primes of powers of square-free monomial ideals
• Symbolic Powers of Monomial Ideals
• The Cohen-Macaulay symbolic Rees algebras for curve singularities
• Effective computation of symbolic powers by jacobian matrices
• Powers of Square-Free Monomial Ideals and Combinatorics
• EDGE IDEALS OF WEIGHTED GRAPHS
• Monomial Ideals
• Monomial Algebras
• Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals
• A Beginner’s Guide to Edge and Cover Ideals
• Edge ideals of oriented graphs
• The Two-Triangle Case of the Acquaintance Graph