  Let E be an elementary abelian p-group of rank r and let k be a field of
characteristic p. We introduce functors F_i from finitely generated kE-modules
of constant Jordan type to vector bundles over projective space of dimension
r-1. The fibers of these functors encode complete information about the Jordan
type of the module. We prove that given any vector bundle of rank s on P^{r-1},
there is a kE-module M of stable constant Jordan type [1]^s such that the
functor F_1 applied to M yields the original vector bundle for p=2 and the
Frobenius twist of the original vector bundle for p>2. We also prove that the
theorem cannot be improved if p is odd, because if M is any module of stable
constant Jordan type [1]^s then the Chern numbers c_1, ... ,c_{p-2} of F_1(M)
are divisible by p.
