Deformations of border bases

DOI10.1007/BF03191188zbMath1190.13022arXiv0710.2641MaRDI QIDQ848648

Martin Kreuzer, Lorenzo Robbiano

Publication date: 4 March 2010

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.2641

zbMATH Keywords

border basisflat deformation

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) 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, Subideal border bases, Canonical Hilbert-Burch matrices for ideals of \(k[x,y\)], Algorithms for checking zero-dimensional complete intersections, Cotangent spaces and separating re-embeddings, Gröbner strata in the Hilbert scheme of points, More elementary components of the Hilbert scheme of points, Some syzygies of the generators of the ideal of a border basis scheme, Computing subschemes of the border basis scheme, Explicit projective embeddings of standard opens of the Hilbert scheme of points, From Oil Fields to Hilbert Schemes, The geometry of border bases, A Polyhedral Characterization of Border Bases, Approximate computation of zero-dimensional polynomial ideals, On border basis and Gröbner basis schemes, On the regularity of the monomial point of a border basis scheme

Uses Software

• CoCoA

Cites Work

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• A description of certain affine open subschemes that form an open covering of \(\text{Hilb}^n_{\mathbb{A}^2_k}\).
• Approximate computation of zero-dimensional polynomial ideals
• Computing border bases
• An elementary construction of the multigraded Hilbert scheme of points
• An elementary, explicit, proof of the existence of Hilbert schemes of points
• Stable border bases for ideals of points
• Description de Hilb sup(n) C{X,Y}
• A stratification of Hilbert schemes by initial ideals and applications
• \(t,q\)-Catalan numbers and the Hilbert scheme.
• Characterizations of border bases
• Reducibility of the families of O-dimensional schemes on a variety
• Numerical Polynomial Algebra