Finite 0-dimensional multiprojective schemes and their ideals

2021/11/11 by Ballico, Edoardo, Guardo, Elena
#13A15 #13D02 #14B15 #14M05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.06480

Abstract

We study finite 0-dimensional schemes in product of multiprojective spaces and their ideals. In particular, we describe the set of generators of the ideal defining a 0-dimensional scheme in the case \mathbb P¹×⋯ ×\mathbb P¹ and in the case \mathbb P^n₁× ⋯ × \mathbb 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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• Deformations of zero-dimensional schemes and applications
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