Finite 0-dimensional multiprojective schemes and their ideals

Abstract

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.