Approximation of holomorphic maps with a lower bound on the rank

Abstract

Let K be a closed polydisc or ball in C, and let Y be a quasi-projective algebraic manifold which is Zariski locally equivalent to C P , or a complement of an algebraic subvariety of codimension ≥ 2 in such a manifold. If r is an integer satisfying (n - r + 1)(p - r + 1) ≥ 2, then every holomorphic map from a neighborhood of K to Y with rank > r at every point of K can be approximated uniformly on K by entire maps C n → Y with rank > r at every point of C.