Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1

DOI10.1142/S0219498819500737zbMath1411.13010arXiv1707.06863OpenAlexW2801692494MaRDI QIDQ5383848

Beatrice Picone, Elena Guardo, Giuseppe Favacchio

Publication date: 20 June 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.06863

zbMATH Keywords

arithmetically Cohen-Macaulaymultiprojective spacesconfiguration of lines

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Linkage, complete intersections and determinantal ideals (13C40) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisors, linear systems, invertible sheaves (14C20) Cohen-Macaulay modules (13C14) Configurations and arrangements of linear subspaces (14N20)

Related Items (3)

Steiner systems and configurations of points ⋮ A numerical property of Hilbert functions and lex segment ideals ⋮ The ACM property for unions of lines in \(\mathbb{P}^1 \times \mathbb{P}^2\)

Uses Software

• CoCoA
• ImplicitizationOfTPSwithGenBasepoints

Cites Work

• Unnamed Item
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• ACM sets of points in multiprojective space
• Cohen-Macaulay monomial ideals of codimension 2
• Resolutions of Stanley-Reisner rings and Alexander duality
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• Bounds on the tensor rank
• Ranks of tensors, secant varieties of Segre varieties and fat points
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• Higher secant varieties of the Segre varieties \(\mathbb P^1\times\dots\times\mathbb P^1\)
• Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1
• Line arrangements and configurations of points with an unexpected geometric property
• Segre Functions in Multiprojective Spaces and Tensor Analysis
• Implicitization of tensor product surfaces in the presence of a generic set of basepoints
• The Minimal Free Resolution of Fat Almost Complete Intersections in ℙ¹ × ℙ¹
• On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces
• Fat Points in ℙ¹× ℙ¹and Their Hilbert Functions
• Higher Secant Varieties of ℙⁿ × ℙ¹Embedded in Bi-Degree (a,b)
• Monomial Ideals
• Asymptotics of linear systems, with connections to line arrangements
• A Beginner’s Guide to Edge and Cover Ideals
• On the Hilbert functions of sets of points in ¹ × ¹ × ¹

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