ACM sets of points in multiprojective space

DOI10.1007/BF03191367zbMath1146.13012arXiv0707.3138OpenAlexW2009890303MaRDI QIDQ934347

Elena Guardo, Adam Van Tuyl

Publication date: 29 July 2008

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

Full work available at URL: https://arxiv.org/abs/0707.3138

zbMATH Keywords

Cohen-Macaulaymultiprojective spaceseparator

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (13)

The K\"ahler Different of a Set of Points in $\mathbb{P}^m\times\mathbb{P}^n$ ⋮ Separators of fat points in \(\mathbb P^n\). ⋮ Finite 0-dimensional multiprojective schemes and their ideals ⋮ Virtual complete intersections in \(\mathbb{P}^1\times\mathbb{P}^1\) ⋮ Separators of arithmetically Cohen-Macaulay fat points \(\mathbb P^1\times \mathbb P^1\) ⋮ Fat lines in \(\mathbb P^3\): powers versus symbolic powers ⋮ Classifying ACM sets of points in \({\mathbb{P}^{1} \times \mathbb{P}^{1}}\) via separators ⋮ Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1 ⋮ Separators of points in a multiprojective space ⋮ On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces ⋮ Separators of fat points in \(\mathbb P^n \times \mathbb P^m\) ⋮ Multiprojective spaces and the arithmetically Cohen–Macaulay property ⋮ The ACM property for unions of lines in \(\mathbb{P}^1 \times \mathbb{P}^2\)

Uses Software

• CoCoA

Cites Work

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• Resolutions of generic points lying on a smooth quadric
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• The regularity of points in multi-projective spaces.
• Sets of points and their conductor
• The border of the Hilbert function of a set of points in \(\mathbb P^{n_1}\times \cdots \times \mathbb P^{n_k}\)
• Multigraded regularity: syzygies and fat points
• Separators of points on algebraic surfaces
• The Hilbert Function of a Reduced K -Algebra
• Points in Generic Position and Conductors of Curves with Ordinary Singularities
• THE DEFINING IDEAL OF A SET OF POINTS IN MULTI-PROJECTIVE SPACE
• Fat points schemes on a smooth quadric

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