Syzygies of Veronese Embeddings

Abstract

We prove that the Veronese embedding φscript O signpn(d): ℙn(Rightwards arrow with hook)ℙN with n ≥ 2, d ≥ 3 does not satisfy property Np (according to Green and Lazarsfeld) if p ≥ 3d - 2. We make the conjecture that also the converse holds. This is true for n = 2 and for n = d = 3.