On the derived category of the Cayley plane

TL;DR

This paper constructs a maximal exceptional collection of 27 homogeneous bundles on the Cayley plane, a key example of a minimal homogeneous projective variety associated with the Lie group E_6.

Contribution

It provides the first explicit description of a maximal exceptional collection on the Cayley plane, advancing understanding of its derived category structure.

Findings

Established a maximal exceptional collection of 27 bundles

Connected the collection to the geometry of the Cayley plane

Enhanced the understanding of derived categories of homogeneous varieties

Abstract

We describe a maximal exceptional collection on the Cayley plane, the minimal homogeneous projective variety of $E_6$. This collection consists in a sequence of 27 irreducible homogeneous bundles.