The Hilbert functions of ACM sets of points in \({\mathbb P}^{n_1} {\times}\dots{\times}{\mathbb P}^{n_k}\)

DOI10.1016/S0021-8693(03)00232-1zbMath1039.13008MaRDI QIDQ1399177

Adam Van Tuyl

Publication date: 30 July 2003

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

zbMATH Keywords

partitionsHilbert functionarithmetically Cohen-Macaulay ringsset of points in multiprojective space

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Projective techniques in algebraic geometry (14N05) Cohen-Macaulay modules (13C14)

Related Items (13)

The K\"ahler Different of a Set of Points in $\mathbb{P}^m\times\mathbb{P}^n$ ⋮ Finite 0-dimensional multiprojective schemes and their ideals ⋮ Virtual complete intersections in \(\mathbb{P}^1\times\mathbb{P}^1\) ⋮ On the Hilbert function of zero-dimensional schemes in \(\mathbb P^{1} \times \mathbb P^{1}\) ⋮ Fat lines in \(\mathbb P^3\): powers versus symbolic powers ⋮ Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1 ⋮ Separators of points in a multiprojective space ⋮ ACM sets of points in multiprojective space ⋮ Scheme-Theoretic Complete Intersections in ℙ¹× ℙ¹ ⋮ Separators of fat points in \(\mathbb P^n \times \mathbb P^m\) ⋮ Some Families of Componentwise Linear Monomial Ideals ⋮ The minimal resolutions of double points in \(\mathbb {P}^1 \times \mathbb P^{1}\) with ACM support ⋮ Minimal Free Resolutions of Zero-dimensional Schemes in ℙ¹ × ℙ¹

Uses Software

• CoCoA

Cites Work

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• On the postulation of 0-dimensional subschemes on a smooth quadric
• Monomial ideals and points in projective space
• Hilbert functions of graded algebras
• Introduction to liaison theory and deficiency modules
• The border of the Hilbert function of a set of points in \(\mathbb P^{n_1}\times \cdots \times \mathbb P^{n_k}\)
• Lifting monomial ideals
• The Hilbert Function of a Reduced K -Algebra

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