  Inspired by very ampleness of Zariski Geometries, we introduce and study the
notion of a very ample family of plane curves in any strongly minimal set, and
the corresponding notion of a very ample strongly minimal set (characterized by
the definability of such a family). We show various basic properties; for
example, any strongly minimal set internal to an expansion of an algebraically
closed field is very ample, and any very ample strongly minimal set
non-orthogonal to a strongly minimal set $Y$ is internal to $Y$. We then apply
these results with Zilber's restricted trichotomy to characterize using very
ampleness those structures $\mathcal M=(M,\dots)$ interpreted in an
algebraically closed field which recover all constructible subsets of powers of
$M$. Next we show that very ample strongly minimal sets admit very ample
families of plane curves of all dimensions, and use this to characterize very
ampleness in terms of definable pseudoplanes. Finally, we show that divisible
strongly minimal groups are very ample, and deduce -- answering an old question
of G. Martin -- that in a pure algebraically closed field, $K$ there are no
reducts between $(K,+,\cdot)$ and $(K, \cdot)$.
