Self-duality of even-characteristic pseudo-ovoids

Determine whether every pseudo-ovoid O in PG(4n − 1, q) for even q is isomorphic to its translation dual.

Background

The tangent spaces of a pseudo-ovoid form a pseudo-ovoid in the dual projective space, called the translation dual. Unlike the odd-characteristic case, where non-isomorphic examples are known, the paper explicitly leaves unresolved whether every even-characteristic pseudo-ovoid is isomorphic to its translation dual.