Search

The complete classification of the orbits on subspaces under the action of the projective stabilizer of (classical) algebraic varieties is a challenging task, and few classifications are complete. We focus on a particular action of PGL (2 , q 2) (and PSL (2 , q 2)) arising from the Hermitian Veronese curve in PG (3 , q 2) , a maximal rational curve embedded on a smooth Hermitian surface with some fascinating properties. The study of its orbits leads to a new construction of quasi-Hermitian surfaces: sets of points with the same combinatorial and geometric properties as a non-degenerate Hermitian surface. [ABSTRACT FROM AUTHOR]