Exceptional sequences of 8 line bundles on (P^1)^3

Abstract

We investigate maximal exceptional sequences of line bundles on (P^1)^3, i.e. those consisting of 2^r elements. For r=3 we show that they are always full, meaning that they generate the derived category. Everything is done in the discrete setup: Exceptional sequences of line bundles appear as special finite subsets s of the Picard group Z^r of (P^1)^r, and the question of generation is understood like a process of contamination of the whole Z^r out of an infectious seed s.