Meromorphic approximation of holomorphic maps into algebraically elliptic projective varieties

Source abstract

We show that holomorphic maps from a neighborhood of a compact set in a Stein space to an algebraically elliptic smooth projective variety can be approximated by meromorphic maps, provided that the map extends continuously to the whole space and the compact set is convex with respect to a submonoid of the Picard group. The proof uses algebraic sprays and their polynomial lifts to affine cones, which we call conic lifts. Rational sprays, which generalize algebraic sprays, extend the result to maps avoiding the exceptional set of a rational spray. We also show that, for smooth projective varieties, the existence of an algebraic spray which is dominating at some point is a birational invariant.