On Hermitian varieties in $\mathrm{PG}(6,q^2)$

Abstract

In this paper we characterize the non-singular Hermitian variety $\mathcal{H}(6,q^2)$ of $\mathrm{PG}(6,q^2)$, $q\ne 2$ among the irreducible hypersurfaces of degree $q+1$ in $\mathrm{PG}(6,q^2)$ not containing solids by the number of its points and the existence of a solid $S$ meeting it in $q^4+q^2+1$ points.

13 pages/revised version