Star-Configurations in ℙ2Having Generic Hilbert Function and the Weak Lefschetz Property

DOI10.1080/00927872.2012.656783zbMath1255.13011OpenAlexW2046301490MaRDI QIDQ2903381

Yong Su Shin

Publication date: 8 August 2012

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

Full work available at URL: https://doi.org/10.1080/00927872.2012.656783

zbMATH Keywords

Hilbert functionsminimal free resolutionsWeak Lefschetz PropertyLefschetz elementsstar-configurations

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Complete intersections (14M10) Low codimension problems in algebraic geometry (14M07)

Related Items (10)

Graded betti numbers and shifts of the symbolic power of a general star configuration in ℙⁿ ⋮ Demailly's conjecture and the containment problem ⋮ Unnamed Item ⋮ The Minimal Free Resolution of a Fat Star-Configuration in ℙⁿ ⋮ A graded minimal free resolution of the $m$-th order symbolic power of a star configuration in $\P^n$ ⋮ The minimal free graded resolution of a star-configuration in \(\mathbb{P}^n\) ⋮ Unnamed Item ⋮ Star-Configurations in ℙⁿand the Weak-Lefschetz Property ⋮ Unnamed Item ⋮ The union of two linear star configurations in \(\mathbb{P}^2\) all have generic Hilbert function

Cites Work

• The Hilbert functions which force the Weak Lefschetz property
• Generic initial ideals and graded Artinian-level algebras not having the weak-Lefschetz property
• \(k\)-configurations in \(\mathbb{P}^3\) all have extremal resolutions
• Some special configurations of points in \(\mathbb P^n\)
• Extremal point sets and Gorenstein ideals
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Ideals of general forms and the ubiquity of the weak Lefschetz property.
• Some algebraic consequences of Green's hyperplane restriction theorems
• The strong Lefschetz property for Artinian algebras with non-standard grading
• On the first infinitesimal neighborhood of a linear configuration of points in \(\mathbb P^2\)
• THE MINIMAL FREE RESOLUTION OF A STAR-CONFIGURATION IN ?ⁿAND THE WEAK LEFSCHETZ PROPERTY
• Generic Initial Ideals, Graded Betti Numbers, andk-Lefschetz Properties
• The hilbert function and the minimal free resolution of some gorenstein ideals of codimension 4

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