Approximation of holomorphic maps by algebraic morphisms

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 -