On generic quadratic forms

Nikita A. Karpenko

Vol. 297 (2018), No. 2, 367–380

DOI: 10.2140/pjm.2018.297.367

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