On the Lefschetz property for quotients by monomial ideals containing squares of variables

DOI10.1080/00927872.2023.2260012arXiv2112.09434OpenAlexW4387164092MaRDI QIDQ6149483

Unnamed Author, Hailong Dao

Publication date: 5 March 2024

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

Full work available at URL: https://arxiv.org/abs/2112.09434

zbMATH Keywords

triangulationGorenstein ringbipartite graphmonomial idealStanley-Reisner ringsimplicial complexArtinian algebraGrünbaum coloringpseudomanifoldsLefschetz propertiesface 2-colorable

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

Cites Work

• A tour of the weak and strong Lefschetz properties
• Smooth monomial Togliatti systems of cubics
• Syzygy bundles on \(\mathbb P^2\) and the weak Lefschetz property
• Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties
• The weak Lefschetz property of equigenerated monomial ideals
• Quadratic Gorenstein algebras with many surprising properties
• Quadrangular embeddings of complete graphs and the even map color theorem
• The Lefschetz properties
• Ideals containing the squares of the variables
• The weak Lefschetz property for monomial ideals of small type
• Monomial ideals, almost complete intersections and the Weak Lefschetz property
• Lefschetz properties for Artinian Gorenstein algebras presented by quadrics
• The Lefschetz property for barycentric subdivisions of shellable complexes
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Gr\"unbaum coloring and its generalization to arbitrary dimension
• Laplace Equations and the Weak Lefschetz Property
• The weak Lefschetz property for quotients by quadratic monomials
• Quadratic Gorenstein rings and the Koszul property I
• Do Sums of Squares Dream of Free Resolutions?
• The regularity of Tor and graded Betti Numbers
• Koszul Gorenstein Algebras From Cohen–Macaulay Simplicial Complexes
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