Nikita A. Karpenko: Unitary grassmannians

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Submission: 2011, Mar 17, revised: 2011, Oct 9

We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.

2010 Mathematics Subject Classification: 14L17; 14C25

Keywords and Phrases: Algebraic groups, quadratic forms, projective homogeneous varieties, Chow groups and motives.

Full text: dvi.gz 41 k, dvi 99 k, ps.gz 866 k, pdf.gz 199 k, pdf 239 k.

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