Vol. 297, No. 2, 2018

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On generic quadratic forms

Nikita A. Karpenko

Vol. 297 (2018), No. 2, 367–380
Abstract

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.

Keywords
algebraic groups, projective homogeneous varieties, Chow groups
Mathematical Subject Classification 2010
Primary: 14C25, 20G15
Milestones
Received: 10 June 2017
Revised: 29 March 2018
Accepted: 18 April 2018
Published: 20 December 2018
Authors
Nikita A. Karpenko
Mathematical & Statistical Sciences
University of Alberta
Edmonton, AB
Canada