Square-free Gröbner degenerations

DOI10.1007/s00222-020-00958-7zbMath1451.13076arXiv1805.11923OpenAlexW3010278121MaRDI QIDQ785935

Matteo Varbaro, Aldo Conca

Publication date: 12 August 2020

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.11923

zbMATH Keywords

Gröbner baseslocal cohomology

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Local cohomology and commutative rings (13D45)

Related Items (38)

Binomial edge ideals of cographs ⋮ Hilbert-Poincaré series of parity binomial edge ideals and permanental ideals of complete graphs ⋮ Lyubeznik numbers of almost complete intersection and linked ideals ⋮ Lower Bounds on Betti Numbers ⋮ Cohomologically Full Rings ⋮ Linear strands of initial ideals of determinantal facet ideals ⋮ Unnamed Item ⋮ Fiber cones of rational normal scrolls are Cohen-Macaulay ⋮ Hamiltonian paths, unit-interval complexes, and determinantal facet ideals ⋮ Local cohomology of binomial edge ideals and their generic initial ideals ⋮ \(N\)-fiber-full modules ⋮ Initially regular sequences and depths of ideals ⋮ A local study of the fiber-full scheme ⋮ Closed binomial edge ideals ⋮ Fiber-full modules and a local freeness criterion for local cohomology modules ⋮ Gorenstein binomial edge ideals ⋮ Induced matchings in strongly biconvex graphs and some algebraic applications ⋮ Gröbner deformations and F‐singularities ⋮ On Rees algebras of 2‐determinantal ideals ⋮ Regularity and multiplicity of toric rings of three-dimensional Ferrers diagrams ⋮ A colorful hochster formula and universal parameters for face rings ⋮ Frobenius methods in combinatorics ⋮ Generic generalized diagonal matrices ⋮ Multidegrees, prime ideals, and non-standard gradings ⋮ \((S_2)\)-condition and Cohen-Macaulay binomial edge ideals ⋮ Lyubeznik and Betti numbers for homogeneous ideals ⋮ Singularities and radical initial ideals ⋮ Binomial edge ideals of small depth ⋮ Almost complete intersection binomial edge ideals and their Rees algebras ⋮ Gröbner deformations ⋮ Betti numbers of toric ideals of graphs: A case study ⋮ On the Betti numbers of edge ideals of skew Ferrers graphs ⋮ Simplicial complexes of small codimension ⋮ Properties of the toric rings of a chordal bipartite family of graphs ⋮ Gröbner Degenerations ⋮ Knutson ideals of generic matrices ⋮ Blow-up algebras of secant varieties of rational normal scrolls ⋮ Connectedness of square-free Groebner deformations

Uses Software

• CoCoA
• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the discrete counterparts of algebras with straightening laws
• On a conjecture by Kalai
• Dualizing complex of the face ring of a simplicial poset
• A criterion for detecting m-regularity
• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Linear spaces, transversal polymatroids and ASL domains
• Gröbner deformations, connectedness and cohomological dimension
• Rings with lexicographic straightening law
• Applications of dualizing complexes to Buchsbaum rings
• Determinantal rings
• The purity of the Frobenius and local cohomology
• Zur lokalen Kohomologie des kanonischen Moduls
• On the diameter of an ideal
• On the diameter of dual graphs of Stanley-Reisner rings and Hirsch type bounds on abstractions of polytopes
• On the extremal Betti numbers of binomial edge ideals of block graphs
• Cartwright-Sturmfels ideals associated to graphs and linear spaces
• Gröbner bases and Stanley decompositions of determinantal ideals
• Extremal Betti numbers and applications to monomial ideals
• On the Dual Graphs of Cohen–Macaulay Algebras
• The Hilbert Scheme of the Diagonal in a Product of Projective Spaces
• F-injective singularities are Du Bois
• F-regularity does not deform
• Multigraded Generic Initial Ideals of Determinantal Ideals
• Universal Gröbner Bases and Cartwright–Sturmfels Ideals
• The Number of Equations Defining a Determinantal Variety
• The Hirsch Conjecture Holds for Normal Flag Complexes
• Universal Grobner Bases for Maximal Minors
• Local cohomology of Du Bois singularities and applications to families
• Connectivity of hyperplane sections of domains

This page was built for publication: Square-free Gröbner degenerations