On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces

The complete classification of the orbits on subspaces under action projective stabilizer (classical) algebraic varieties is a challenging task, and few classifications are complete. We focus particular PGL(2,q2) (and PSL(2,q2)) arising from Hermitian Veronese curve in PG(3,q2), maximal rational embedded smooth surface with some fascinating properties. study its leads to new construction quasi-Hermitian surfaces: sets points same combinatorial geometric properties as non-degenerate surface.