Tate resolutions for Segre embeddings

Abstract

We give an explicit description of the terms and differentials of the Tate resolution of sheaves arising from Segre embeddings of ${\mathbb{P}}^a\times {\mathbb{P}}^b$. We prove that the maps in this Tate resolution are either coming from Sylvester-type maps, or from Bezout-type maps arising from the so-called toric Jacobian.