The border of the Hilbert function of a set of points in \(\mathbb P^{n_1}\times \cdots \times \mathbb P^{n_k}\)

DOI10.1016/S0022-4049(02)00072-5zbMath1019.13008arXivmath/0112185OpenAlexW1526149345MaRDI QIDQ1861461

Adam Van Tuyl

Publication date: 9 March 2003

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0112185

zbMATH Keywords

sets of pointsmultigraded Hilbert function

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Matrices of integers (15B36)

Related Items (13)

Multigraded Hilbert functions and toric complete intersection codes ⋮ The K\"ahler Different of a Set of Points in $\mathbb{P}^m\times\mathbb{P}^n$ ⋮ Implicitization of tensor product surfaces in the presence of a generic set of basepoints ⋮ The Hilbert functions of ACM sets of points in \({\mathbb P}^{n_1} {\times}\dots{\times}{\mathbb P}^{n_k}\) ⋮ Finite 0-dimensional multiprojective schemes and their ideals ⋮ On the Hilbert functions of sets of points in ¹ × ¹ × ¹ ⋮ On the Hilbert function of zero-dimensional schemes in \(\mathbb P^{1} \times \mathbb P^{1}\) ⋮ The regularity of points in multi-projective spaces. ⋮ Separators of points in a multiprojective space ⋮ ACM sets of points in multiprojective space ⋮ Separators of fat points in \(\mathbb P^n \times \mathbb P^m\) ⋮ A numerical property of Hilbert functions and lex segment ideals ⋮ The number of solutions to some systems of equations

Uses Software

• CoCoA

Cites Work

• On the postulation of 0-dimensional subschemes on a smooth quadric
• The ideal of forms vanishing at a finite set of points in \({\mathbb{P}}^ n\)
• Monomial ideals and points in projective space
• Hilbert functions of graded algebras
• The minimal resolution conjecture
• Resolutions of generic points lying on a smooth quadric
• Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions
• The Hilbert function of generic plane sections of curves of \({\mathbb P}^ 3\)
• The Hilbert Function of a Reduced K -Algebra
• An alternative to the Hilbert function for the ideal of a finite set of points in \(\mathbb P^n\)
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