The geometry of border bases

DOI10.1016/j.jpaa.2010.11.011zbMath1216.13018arXiv1004.1044OpenAlexW2963486400MaRDI QIDQ534027

Martin Kreuzer, Lorenzo Robbiano

Publication date: 10 May 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.1044

zbMATH Keywords

border bases schemesflat families of border basesflat families of schemespunctual Hilbert schemes

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) Algebraic moduli problems, moduli of vector bundles (14D20) Deformations and infinitesimal methods in commutative ring theory (13D10) Formal methods and deformations in algebraic geometry (14D15)

Related Items

The close relation between border and Pommaret marked bases, Cotangent spaces and separating re-embeddings, Computing subschemes of the border basis scheme, On the regularity of the monomial point of a border basis scheme

Uses Software

• CoCoA
• ApCoCoA

Cites Work

• Deformations of border bases
• An elementary construction of the multigraded Hilbert scheme of points
• An elementary, explicit, proof of the existence of Hilbert schemes of points
• On border basis and Gröbner basis schemes
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• Recovering the good component of the Hilbert scheme
• From Oil Fields to Hilbert Schemes
• Multigraded Hilbert schemes
• Numerical Polynomial Algebra
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