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Approximation of holomorphic maps by algebraic morphisms

J. Bochnak, W. Kucharz (2003)

Annales Polonici Mathematici

Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.

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