Finite 0-dimensional multiprojective schemes and their ideals

摘要

In this paper, 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 ℙ1×⋯×ℙ1 and in the case ℙn1×⋯×ℙnk with ni∈{1,2} for all i. We also check very ampleness for zero-dimensional schemes of general points in the multiprojective spaces.