On the derived category of the Cayley plane II

Faenzi, Daniele; Manivel, Laurent

doi:10.1090/S0002-9939-2014-12312-4

On the derived category of the Cayley plane II
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by Daniele Faenzi and Laurent Manivel PDF

Proc. Amer. Math. Soc. 143 (2015), 1057-1074 Request permission

Abstract:

We find a full strongly exceptional collection for the Cayley plane $\mathbb {O}\mathbb {P}^2$, the simplest rational homogeneous space of the exceptional group $E_6$. This collection, closely related to the one given by the second author in 2011, consists of $27$ vector bundles which are homogeneous for the group $E_6$, and is a minimal Lefschetz collection with respect to the minimal equivariant embedding of $\mathbb {O}\mathbb {P}^2$.

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