Knotting of Algebraic Curves in CP2

Abstract

I construct "fake algebraic curves" in $C{p}^2$. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset C{p}^2$ 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 $C{p}^2-F$. This gives an answer to Problem 4.110 of Kirby's list.

9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the Intro