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Journal of the Ramanujan Mathematical Society

Volume 28, Issue 2, June 2013  pp. 213–222.

Orthogonal and symplectic grassmannians of division algebras

Authors Nikita A. Karpenko
Author institution: Université Pierre et Marie Curie, Institute de Mathématiques de Jussieu, Paris, France

Summary:  We consider a central division algebra (over a field) endowed with a quadratic pair or with a symplectic involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. This covers a recent conjecture raised by M. Zhykhovich. The remaining related projective homogeneous varieties are 2-compressible in general.

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