On linear morphisms of product spaces

Abstract

Let $\chi$ be a linear morphism of the product of two projective spaces $PG(n,F)$ and $PG(m,F)$ into a projective space. Let $\gamma$ be the Segre embedding of such a product. In this paper we give some sufficient conditions for the existence of an automorphism $\alpha$ of the product space and a linear morphisms of projective spaces $\varphi$, such that $\gamma \varphi =\alpha \chi$.