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arXiv · 2206.14525

On the Derived Category of the Cayley Grassmannian

Lyalya Guseva
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Abstract

We construct a full exceptional collection consisting of vector bundles in the derived category of coherent sheaves on the so-called Cayley Grassmannian, the subvariety of the Grassmannian $\mathrm{Gr}(3, 7)$ parameterizing 3-subspaces that are annihilated by a general 4-form. The main step in the proof of fullness is a construction of two self-dual vector bundles which is obtained from two operations with quadric bundles that might be interesting in themselves.

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Lyalya Guseva. 2022-06-29. On the Derived Category of the Cayley Grassmannian. https://arxiv.org/abs/2206.14525

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