Strongly stable ideals and Hilbert polynomials

DOI10.2140/jsag.2019.9.1zbMath1422.13024arXiv1406.6924OpenAlexW3101770878MaRDI QIDQ2325359

Paolo Lella

Publication date: 25 September 2019

Published in: The Journal of Software for Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.6924

zbMATH Keywords

Hilbert schemeHilbert polynomialGotzmann numberBorel-fixed idealstrongly stable ideal

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to commutative algebra (13-04) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items (6)

The Gröbner fan of the Hilbert scheme ⋮ On the tangent space to the Hilbert scheme of points in 𝐏³ ⋮ Syzygies in Hilbert schemes of complete intersections ⋮ Combinatorial decompositions for monomial ideals ⋮ Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces ⋮ StronglyStableIdeals

Uses Software

• Macaulay2

Cites Work

• On the functoriality of marked families
• Double-generic initial ideal and Hilbert scheme
• Segments and Hilbert schemes of points
• Rational components of Hilbert schemes
• Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes
• Upgraded methods for the effective computation of marked schemes on a strongly stable ideal
• A Borel open cover of the Hilbert scheme
• Flat families by strongly stable ideals and a generalization of Gröbner bases
• Extensors and the Hilbert scheme
• Algorithms for strongly stable ideals
• Betti numbers, castelnuovo mumford regularity, and generalisations of macaulay's theorem
• An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme
• Macaulay-like marked bases

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