Regularity of even-characteristic pseudo-ovoids

Determine whether every pseudo-ovoid in PG(4n − 1, q) for even q is regular.

Background

Pseudo-ovoids generalize ovoids by replacing points with (n − 1)-dimensional subspaces. Regular pseudo-ovoids are obtained by field reduction from ovoids in PG(3, q^n). In even characteristic, all known pseudo-ovoids are regular, but the paper does not prove that every such pseudo-ovoid is regular.