Rational approximation of holomorphic maps

Let X be a complex nonsingular affine algebraic variety, K a compact holomorphically convex subset of X , and Y a homogeneous complex man-ifold for some complex linear algebraic group. We prove that a holomorphic map f : K-+ Y can be uniformly approximated on K by regular maps K-+ Y if and only if f is homotopic to a regular map K-+ Y. However, it may happen that a null homotopic holomorphic map K-+ Y does not admit uniform approximation on K by regular maps X-+ Y. Here, a map & phi;: K-+ Y is called holomorphic (resp. regular) if there exist an open (resp. a Zariski open) neighborhood U C X of K and a holomorphic (resp. regular) map & phi;e: U-+ Y such that & phi;e|K = & phi;.