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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.
J. Bochnak, and W. Kucharz. "Approximation of holomorphic maps by algebraic morphisms." Annales Polonici Mathematici 80.1 (2003): 85-92. <http://eudml.org/doc/280177>.
@article{J2003, abstract = {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.}, author = {J. Bochnak, W. Kucharz}, journal = {Annales Polonici Mathematici}, keywords = {algebraic curve; algebraic surface; holomorphic map; rational map; approximation}, language = {eng}, number = {1}, pages = {85-92}, title = {Approximation of holomorphic maps by algebraic morphisms}, url = {http://eudml.org/doc/280177}, volume = {80}, year = {2003}, }
TY - JOUR AU - J. Bochnak AU - W. Kucharz TI - Approximation of holomorphic maps by algebraic morphisms JO - Annales Polonici Mathematici PY - 2003 VL - 80 IS - 1 SP - 85 EP - 92 AB - 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. LA - eng KW - algebraic curve; algebraic surface; holomorphic map; rational map; approximation UR - http://eudml.org/doc/280177 ER -