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arXiv · 2108.11806

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

Klaus Altmann·Martin Altmann
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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.

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Klaus Altmann, Martin Altmann. 2021-08-26. Exceptional sequences of 8 line bundles on (P^1)^3. https://arxiv.org/abs/2108.11806

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