On syzygies of Segre embeddings of $P^1\times P^1$

Abstract

We construct a nonminimal graded free resolution of Segre embeddings of $P^1\times P^1$, although we don't compute all maps. We use this to prove an explicit formula for certain nonzero entries in the graded Betti table, at the end of the first row. We work over an arbitrary field $k$.