Exceptional collections on isotropic Grassmannians

By Alexander Kuznetsov, Alexander Polishchuk. 2011

55 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e2ab3948d8ee72c922ad97094e537c3b6c5c7385

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Lectures on Non-commutative K3 Surfaces, Bridgeland Stability, and Moduli Spaces (2018, result): “ogonal decompositions for the derived categories of Grassmannians over the integers are studied. For later use, we need a diﬀerent exceptional collection, described more recently in [Fon15] (see also [KuPo16] for related results). We assume that gcd(k,n) = 1. Then we have a semiorthogonal decomposit”
Semiorthogonal decompositions in algebraic geometry (2014, background): “ll exceptional collection in the equivariant category. It would be extremely useful to ﬁnd a way to transform it into a full exceptional collection in the usual category. In some sense the results of [KP11] can be considered as an example of such an approach. Another very important question is to ﬁn”