Segments and Hilbert schemes of points

DOI10.1016/j.disc.2011.07.011zbMath1243.14007arXiv1003.2951OpenAlexW2054512056MaRDI QIDQ641200

Francesca Cioffi, Paolo Lella, Maria Grazia Marinari, Margherita Roggero

Publication date: 21 October 2011

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.2951

zbMATH Keywords

Hilbert scheme of pointsBorel idealdegrevlex term orderGotzmann numberGröbner stratumsegment ideal

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Parametrization (Chow and Hilbert schemes) (14C05)

Related Items (20)

On the functoriality of marked families ⋮ Algorithms for strongly stable ideals ⋮ Smoothable Gorenstein Points Via Marked Schemes and Double-generic Initial Ideals ⋮ Borel degenerations of arithmetically Cohen–Macaulay curves in ℙ³ ⋮ Minimal Castelnuovo–Mumford Regularity for a Given Hilbert Polynomial ⋮ The Gröbner fan of the Hilbert scheme ⋮ On almost revlex ideals with Hilbert function of complete intersections ⋮ Hilbert schemes with two Borel-fixed points in arbitrary characteristic ⋮ Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial ⋮ Syzygies in Hilbert schemes of complete intersections ⋮ The ubiquity of smooth Hilbert schemes ⋮ When the positivity of the \(h\)-vector implies the Cohen-Macaulay property ⋮ Combinatorial decompositions for monomial ideals ⋮ Double-generic initial ideal and Hilbert scheme ⋮ Bar code for monomial ideals ⋮ A general framework for Noetherian well ordered polynomial reductions ⋮ Macaulay-like marked bases ⋮ Strongly stable ideals and Hilbert polynomials ⋮ The Locus of Points of the Hilbert Scheme with Bounded Regularity ⋮ Hilbert schemes with two Borel-fixed points

Uses Software

• StronglyStableIdeals

Cites Work

• A criterion for detecting m-regularity
• Rational components of Hilbert schemes
• Hilbert schemes of 8 points
• Gröbner bases and Hilbert schemes. I
• Some properties of Borel ideals
• A stratification of Hilbert schemes by initial ideals and applications
• Flat families by strongly stable ideals and a generalization of Gröbner bases
• Generic initial ideals of points and curves
• Borel ideals in three variables
• Connectedness of Hilbert scheme
• Ideals with an assigned initial ideal
• Homogeneous varieties for Hilbert schemes
• Bounds for multiplicities
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