Knotting of algebraic curves in [formula omitted

Abstract

For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces F⊂ CP 2 homeomorphic to a non-singular algebraic curve of degree 2 k, realizing the same homology class as such a curve and having abelian fundamental group π 1( CP 2⧹F) . This gives an answer to Problem 4.110 in the Kirby list (Kirby, Problems in low-dimensional topology, in: W. Kazez (Ed.), Geometric Topology, AMS/IP Stud. Adv. Math. vol 2.2, Amer. Math. Soc., Providence, 1997).