Exceptional sequences of 8 line bundles on (P¹)³

2021/08/26 by Altmann, Klaus, Altmann, Martin
#06A07 #14M25 #18G80 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.11806

Abstract

We investigate maximal exceptional sequences of line bundles on (P¹)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 (P¹)^r, and the question of generation is understood like a process of contamination of the whole Z^r out of an infectious seed s.

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