Exceptional collections for Grassmannians of isotropic lines

Abstract

We construct a full exceptional collection of vector bundles in the derived category of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in a symplectic vector space of dimension $2n$ and in the derived category of coherent sheaves on the Grassmannian of isotropic two-dimensional subspaces in an orthogonal vector space of dimension $2n+1$ for all $n$.

26 pages; thoroughly revised - a construction of a full exceptional collection for the orthogonal isotropic Grassmannian OGR(2,2n+1) is included

References in corpus (2)

• Homological projective duality for Grassmannians of lines
• Lefschetz decompositions and Categorical resolutions of singularities

Cited by in corpus (42)

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• Derived equivalences for the flops of type $C_2$ and $A_4^G$ via mutation of semiorthogonal decomposition
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• The Pfaffian-Grassmannian derived equivalence
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• Exceptional collections, t-structures, and categorical action of shifted $q=0$ affine algebra, ${\mathfrak{sl}}_2$ case