Let $V$ be a Zariski open subset of an affine variety over $\mathbb{Z}$, and let $f: V \to P$ be a morphism into a projective space $P$ over $\mathbb{Z}[i]$. Assume there given a projective hypersurface $Z \subset P$ given by the vanishing of a homogeneous polynomial with coefficients in $\mathbb{Z}[i]$, and that
$f(V) \cap Z = \phi$
We would like to consider these objects over a commutative ring $A$ with $1$, in which $-1$ is not a square. If we now let $V_A$ be the variety $V$ defined now over $A$, let $P_A$ and $Z_A$ be the projective varieties $P$ and $Z$ respectively defined now over $A[i]$, and denote by
$f_A: V_A \to P_A$
the map corresponding to $f$. Under what conditions on $V$, $P$, $f$ and $A$, do we have
$f_A(V_A) \cap Z_A = \phi$ ?