On the Derived Category of the Cayley Grassmannian

DOI10.1134/S0001434623010169arXiv2206.14525MaRDI QIDQ6403500

L. A. Guseva

Publication date: 29 June 2022

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 $mathrmGr(3,7)$ 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.

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Derived categories of sheaves, dg categories, and related constructions in algebraic geometry (14F08)

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