For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as such a curve and having abelian fundamental group p1(\Cp2\stmin F). It is a special case of a more general theorem, which concerns for instance those algebraic curves, A, in a simply connected algebraic surface, X, which admit irreducible degenerations to a curve A0, with a unique singularity of the type X9, and such that A\cite A>16.

For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as such a curve and having abelian fundamental group p1(\Cp2\stmin F). It is a special case of a more general theorem, which concerns for instance those algebraic curves, A, in a simply connected algebraic surface, X, which admit irreducible degenerations to a curve A0, with a unique singularity of the type X9, and such that A\cite A>16.