Exceptional collections on isotropic Grassmannians

Abstract

We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.

v1: 51 page; v2: 55 pages, to appear in JEMS

References in corpus (7)

• Hochschild homology and semiorthogonal decompositions
• Determinantal Barlow surfaces and phantom categories
• On the derived category of the classical Godeaux surface
• Derived categories of Burniat surfaces and exceptional collections
• Exceptional collections of line bundles on the Beauville surface
• Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)
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Cited by in corpus (16)

• Semiorthogonal decompositions in algebraic geometry
• Exceptional collections, and the Neron-Severi lattice for surfaces
• Full exceptional collections on Lagrangian Grassmannians
• Residual categories for (co)adjoint Grassmannians in classical types
• On a conjecture of Kuznetsov and Polishchuk
• Exceptional collections of line bundles on projective homogeneous varieties
• Tilting objects on twisted forms of some relative flag varieties
• Dual exceptional collections on Lagrangian Grassmannians
• On the derived category of $\mathrm{IGr}(3,8)$
• On the bounded derived category of $\mathsf{IGr}(3,7)$
• Categorical dimension of birational automorphisms and filtrations of Cremona groups
• Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
• On the derived category of the adjoint Grassmannian of type F
• Derived Categories of Grassmannians: a Survey
• On the big quantum cohomology of coadjoint varieties
• Weil transfer of noncommutative motives