Approximation of holomorphic maps by algebraic morphisms

Volume 80 / 2003

J. Bochnak, W. Kucharz Annales Polonici Mathematici 80 (2003), 85-92 MSC: 14A10, 32H05. DOI: 10.4064/ap80-0-5


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. BochnakDepartment of Mathematics
    Vrije Universiteit
    De Boelelaan 1081a
    1081 HV Amsterdam, The Netherlands
  • W. KucharzDepartment of Mathematics and Statistics
    University of New Mexico
    Albuquerque, NM 87131-1141, U.S.A.

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