  A non-singular connected algebraic curve $A$ in a simply connected algebraic
surface $X$ can be knotted so that its homology class and the fundamental group
of its complement in $X$ is preserved, provided $A$ is sufficiently complex
(not too ``rigid'').
  For example, it is true if $A$ admits a degeneration to an irreducible curve
$A_0$ having a unique singularity of the type $X_9$ (a non-degenerate quadriple
point), or more complicated one, and $A.A>16$.
  This generalizes the previous result of the author which concerns the curves
in $CP^2$ of degree $d>4$ (the old preprint is included as a part of the
current one).
