Resolutions of Segre embeddings of projective spaces of any dimension

This paper deals with syzygies of the ideals of Segre embeddings. Let d≥3d≥3 and n1,…,nd∈N−{0}. We prove that OPn1×⋯×Pnd(1,…,1) satisfies Green–Lazarsfeld’s property NpNp if and only if p≤3p≤3.