The ACM property for unions of lines in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>

Favacchio, Giuseppe; Migliore, Juan

doi:10.1016/j.jpaa.2021.106739

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Properties of Arithmetically Cohen Macaulay (ACM) sets of points in P 1 × P 1 and their combinatorial structure are collected and described in [16]. Natural generalizations are the study ACM sets of (reduced) points in P n × P m and P 1 × • • • × P 1 that also can be characterized using their combinatorial structures (see for instance [6,7,8,15,20,26,27]). As we can see from the literature, most of the known results are about the ACM property.…”

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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Hadamard Products of Symbolic Powers and Hadamard Fat Grids

et al. 2023

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In this paper we address the question if, for points $$P, Q \in \mathbb {P}^{2}$$ P , Q ∈ P 2 , $$I(P)^{m} \star I(Q)^{n}=I(P \star Q)^{m+n-1}$$ I ( P ) m ⋆ I ( Q ) n = I ( P ⋆ Q ) m + n - 1 and we obtain different results according to the number of zero coordinates in P and Q. Successively, we use our results to define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicities. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed.

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Finite 0-dimensional multiprojective schemes and their ideals

Ballico

Guardo

2022

J. Algebra Appl.

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In this paper, we study finite [Formula: see text]-dimensional schemes in product of multiprojective spaces and their ideals. In particular, we describe the set of generators of the ideal defining a [Formula: see text]-dimensional scheme in the case [Formula: see text] and in the case [Formula: see text] with [Formula: see text] for all [Formula: see text]. We also check very ampleness for zero-dimensional schemes of general points in the multiprojective spaces.

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The ACM property for unions of lines in P1×P2

Cited by 3 publications

References 17 publications

Finite $0$-dimensional multiprojective schemes and their ideals

Finite $0$-dimensional multiprojective schemes and their ideals

Hadamard Products of Symbolic Powers and Hadamard Fat Grids

Finite 0-dimensional multiprojective schemes and their ideals

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