  I construct "fake algebraic curves" in $Cp^2$.
  More precisely, for any k>2, I construct infinitely many pairwise smoothly
non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset
Cp^2$ homeomorphic to a non-singular algebraic curve of degree 2k, realizing
the same homology class as such a curve and having abelian fundamental group of
the complement $Cp^2-F$.
  This gives an answer to Problem 4.110 of Kirby's list.
