Scheme-Theoretic Complete Intersections in ℙ<sup>1</sup>× ℙ<sup>1</sup>

Giuffrida, Sergio; Maggioni, Renato; Zappalà, Giuseppe

doi:10.1080/00927872.2011.605410

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…A first step of studying 0-dimensional schemes in product of multiprojective spaces can be considered [11], where the authors investigated the structure of the Hilbert function of a 0-dimensional schemes X in P 1 × P 1 and studied the relationship between the Hilbert function and the cohomology groups of the ideal sheaf I X . It followed also the study of the resolution of 0-dimensional schemes which are generic in P 1 × P 1 (see for instance [12,13]) and the beginning of the study of virtual (scheme-theoretic) complete intersections in P 1 × P 1 in [14].…”

Section: Introductionmentioning

confidence: 99%

Finite $0$-dimensional multiprojective schemes and their ideals

Ballico¹,

Guardo²

2021

Preprint

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We study finite 0-dimensional schemes in product of multiprojective space and their ideals. In particular, we describe the set of generators of the ideal defining a 0-dimensional scheme in the case P 1 × • • • × P 1 and in the case P n 1 × • • • × P n k with n i ∈ {1, 2} for all i. We also check very ampleness for zero-dimensional schemes of general points in the multiprojective spaces.

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Section: Introductionmentioning

confidence: 99%

Finite $0$-dimensional multiprojective schemes and their ideals

Ballico¹,

Guardo²

2021

Preprint

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Homological invariants

Guardo¹,

Tuyl²

2015

Arithmetically Cohen-Macaulay Sets of Points in P^1 X P^1

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On the Hilbert function of a finite scheme contained in a quadric surface

Maican

2023

Collect. Math.

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Let X be a zero-dimensional scheme contained in a multiprojective space. Let s i be the length of the projection of X onto the i-th component of the multiprojective space. A result of A. Van Tuyl states that the Hilbert function of X, in the case when X is reduced, is completely determined by its restriction to the product of the intervals [0, s i − 1]. We prove that the same is also true for non-reduced schemes X.

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Scheme-Theoretic Complete Intersections in ℙ¹× ℙ¹

Cited by 4 publications

References 9 publications

Finite $0$-dimensional multiprojective schemes and their ideals

Finite $0$-dimensional multiprojective schemes and their ideals

Homological invariants

On the Hilbert function of a finite scheme contained in a quadric surface

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Scheme-Theoretic Complete Intersections in ℙ1× ℙ1

Cited by 4 publications

References 9 publications

Finite $0$-dimensional multiprojective schemes and their ideals

Finite $0$-dimensional multiprojective schemes and their ideals

Homological invariants

On the Hilbert function of a finite scheme contained in a quadric surface

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Product

Resources

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Scheme-Theoretic Complete Intersections in ℙ¹× ℙ¹