Exceptional sequences of 8 line bundles on (P1)3

Abstract

We investigate maximal exceptional sequences of line bundles on (P1)r, i.e., those consisting of 2r 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 Zr of (P1)r, and the question of generation is understood like a process of contamination of the whole Zr out of an infectious seed s.