Journal of the European Mathematical Society

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Volume 18, Issue 3, 2016, pp. 507–574
DOI: 10.4171/JEMS/596

Exceptional collections on isotropic Grassmannians

Alexander Kuznetsov[1] and Alexander Polishchuk[2]

(1) Steklov Mathematical Institute, Moscow, Russian Federation
(2) University of Oregon, Eugene, United States

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.

Keywords: Exceptional collection, derived category of sheaves, isotropic Grassmannian

Kuznetsov Alexander, Polishchuk Alexander: Exceptional collections on isotropic Grassmannians. J. Eur. Math. Soc. 18 (2016), 507-574. doi: 10.4171/JEMS/596