1999/07/16 by Sergey Finashin, Finashin, Sergey
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT
paper · pdf · doi:10.48550/arxiv.math/9907108
9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the Intro
openalex publication_date 1999/07/16 · arxiv created 1999/07/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I construct "fake algebraic curves" in Cp2. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces F⊂ Cp2 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 Cp2-F. This gives an answer to Problem 4.110 of Kirby's list.