Minimally generating ideals defining certain tangent cones

DOI10.1016/0021-8693(82)90101-6zbMath0502.14001OpenAlexW1965265130MaRDI QIDQ1172676

Anthony V. Geramita, Ferruccio Orecchia

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0021-8693(82)90101-6

zbMATH Keywords

Cohen-Macaulay typetangent conesnumber of generators of ideals of points

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Singularities in algebraic geometry (14B05) Singularities of curves, local rings (14H20) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Low codimension problems in algebraic geometry (14M07) Relevant commutative algebra (14A05)

Related Items (24)

On Rational Varieties Smooth Except at a Seminormal Singular Point ⋮ Standard bases of perfect homogeneous polynomial ideals of height 2 ⋮ Open problems on syzygies and Hilbert functions ⋮ Maximal rank for \(T_{\mathbb{P}^n}\) ⋮ Derivations and the Cohen-Macaulay type of points in generic position in n-space ⋮ Star configurations on generic hypersurfaces ⋮ Reduced Tangent Cones and Conductor at Multiplanar Isolated Singularities ⋮ The Cohen-Macaulay type of points in generic position ⋮ On the irreducibility of multivariate subresultants. ⋮ Multiple points, scheme rank and symmetric tensor rank ⋮ On the homogeneous ideal of finite sets in \(\mathbb{P}^ n\) ⋮ Cartesian squares and ordinary singularities of curves ⋮ On certain classes of curve singulariries with reduced tangent cone ⋮ Betti numbers of points in projective space ⋮ Homaloidal nets and ideals of fat points I ⋮ Generators for the homogeneous ideal of s general points in \({\mathbb{P}}_ 3\) ⋮ The ideal generation conjecture for general rational projective curves ⋮ Betti numbers of compressed level algebras ⋮ On the defining equations of points in general position in \({\mathbb{P}}^ n\) ⋮ The ideal of forms vanishing at a finite set of points in \({\mathbb{P}}^ n\) ⋮ Chudnovsky’s conjecture and the stable Harbourne–Huneke containment ⋮ Monomial ideals and points in projective space ⋮ Hilbert functions and Betti numbers in a flat family ⋮ Resolutions of ideals of quasiuniform fat point subschemes of 𝐏²

Cites Work

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• One-dimensional local rings with reduced associated graded ring and their Hilbert functions
• On the Cohen-Macaulay type of s-lines in \(A^{n+1}\)
• On equations defining arithmetically Cohen-Macaulay schemes. II
• Der kanonische Modul eines Cohen-Macaulay-Rings. (The canonical moduls of a Cohen-Macaulay-ring)
• Generators for certain ideals in regular rings of dimension three
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• On the equations defining tangent cones
• Ordinary Singularities of Algebraic Curves
• Points in Generic Position and Conductors of Curves with Ordinary Singularities

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