CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES

Abstract

We characterize Hermitian cones among the surfaces of degree$q+1$of$\text{PG}(3,q^{2})$by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of$\text{PG}(4,q^{2})$among quasi-Hermitian ones.