2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78836I 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.9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the IntroGeometric TopologyAlgebraic Geometrytext