The Lefschetz properties of monomial complete intersections in positive characteristic

DOI10.1016/j.jalgebra.2012.07.015zbMath1271.13010arXiv1111.4979OpenAlexW2059610094MaRDI QIDQ1946098

David II Cook

Publication date: 17 April 2013

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

Full work available at URL: https://arxiv.org/abs/1111.4979

zbMATH Keywords

Positive characteristicLefschetz propertiesComplete Intersections

Mathematics Subject Classification ID

Linkage, complete intersections and determinantal ideals (13C40) Syzygies, resolutions, complexes and commutative rings (13D02) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (17)

An algebraic approach to finite projective planes ⋮ The weak Lefschetz property for monomial ideals of small type ⋮ The EGH Conjecture and the Sperner property of complete intersections ⋮ The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets ⋮ Quadratic Gorenstein algebras with many surprising properties ⋮ The strong Lefschetz property in codimension two ⋮ On the degrees of relations on \(x_1^{d_1}, \dots, x_n^{d_n},(x_1 + \dots + x_n)^{d_{n + 1}}\) in positive characteristic ⋮ Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties ⋮ On the structure of monomial complete intersections in positive characteristic ⋮ On the weak Lefschetz property for artinian Gorenstein algebras of codimension three ⋮ The strong Lefschetz property of monomial complete intersections in two variables ⋮ Unnamed Item ⋮ The weak Lefschetz property for Artinian Gorenstein algebras of codimension three ⋮ Interpolation and the weak Lefschetz property ⋮ A note on a conjecture regarding the weak Lefschetz property of a special class of Artinian algebras ⋮ Artinian algebras and Jordan type ⋮ An Artinian Quotient of the Coordinate Ring of a Complete Intersection in ℙⁿHaving the Weak Lefschetz Property

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Trivariate monomial complete intersections and plane partitions
• Monomial complete intersections, the weak Lefschetz property and plane partitions
• The Hilbert functions which force the Weak Lefschetz property
• Syzygy bundles on \(\mathbb P^2\) and the weak Lefschetz property
• Looking out for stable syzygy bundles
• The determinants of certain matrices arising from the Boolean lattice
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Ideals of general forms and the ubiquity of the weak Lefschetz property.
• Product evaluations of Lefschetz determinants for Grassmannians and of determinants of multinomial coefficients
• The weak Lefschetz property, monomial ideals, and lozenges
• A note on the weak Lefschetz property of monomial complete intersections in positive characteristic
• Mason's theorem and syzygy gaps
• A class of Hilbert series and the strong Lefschetz property
• Monomial ideals, almost complete intersections and the Weak Lefschetz property
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• On Complete Intersections and Their Hilbert Functions
• On the shape of a pure 𝑂-sequence

This page was built for publication: The Lefschetz properties of monomial complete intersections in positive characteristic