Approximation of holomorphic maps by algebraic morphisms
Volume 80 / 2003
Annales Polonici Mathematici 80 (2003), 85-92
MSC: 14A10, 32H05.
DOI: 10.4064/ap80-0-5
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.
