Resolutions of Segre embeddings of projective spaces of any dimension

This paper deals with syzygies of Segre embeddings. Let d >=3 and n_1, …, n_d nonzero natural numbers. We prove that O(1,…, 1) on the product of P^{n_1}, …,P^{n_d} satisfies Property N_p if and only if p <= 3.