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Proceedings of the London Mathematical Society Advance Access published online on March 12, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdm056
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© 2007 London Mathematical Society

Exceptional collections for Grassmannians of isotropic lines

Alexander Kuznetsov

Algebra Section
Steklov Mathematical Institute
8 Gubkin street, Moscow 119991
Russia

Received 11 January 2007. Revision received 15 October 2007.

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

2000 Mathematics Subject Classification 14M15, 18E30.

To Miles Reid on the occasion of his 60th birthday

The author was partially supported by RFFI grant 05-01-01034, INTAS 05-1000008-8118, Russian Presidential grant for young scientists no. MK-6122.2006.1, the Russian Science Support Foundation, CRDF Award no. RUM1-2661-MO-05, and he gratefully acknowledges of the support of the Pierre Deligne fund based on his 2004 Balzan prize in mathematics.


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