karpenko at ualberta.ca

Submission: 2017, Jun 11, revised: 2017, Oct. 20

Based on Totaro's computation of the Chow ring of classifying spaces for orthogonal groups, we compute the Chow rings of all orthogonal Grassmannians associated with a generic quadratic form of any dimension. This closes the gap between the known particular cases of the quadric and the highest orthogonal Grassmannian. We also relate two different notions of generic quadratic forms.

2010 Mathematics Subject Classification: 20G15; 14C25

Keywords and Phrases: Algebraic groups; projective homogeneous varieties; Chow groups.

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