Addendum to: Generically split projective homogeneous varieties

TL;DR

This paper extends previous work on classifying projective homogeneous varieties by removing characteristic restrictions and completing the classification for the case of + type orthogonal groups.

Contribution

It generalizes earlier results to all characteristics and finalizes the classification for + type orthogonal groups.

Findings

Removed restrictions on the base field's characteristic.

Completed the classification for + type orthogonal groups.

Extended the applicability of the previous classification results.

Abstract

In this addendum we generalize some results of our article "Generically split projective homogeneous varieties", Duke Math. J. 152 (2010), no. 1, 155-173. More precisely, we remove all restrictions on the characteristic of the base field and complete our classification by the last missing case, namely $\PGO_{2n}^+$.