English

Knotting of Algebraic Curves in CP2

Geometric Topology 2007-05-23 v3 Algebraic Geometry

Abstract

I construct "fake algebraic curves" in Cp2Cp^2. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces FCp2F\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 Cp2FCp^2-F. This gives an answer to Problem 4.110 of Kirby's list.

Keywords

Cite

@article{arxiv.math/9907108,
  title  = {Knotting of Algebraic Curves in CP2},
  author = {Sergey Finashin},
  journal= {arXiv preprint arXiv:math/9907108},
  year   = {2007}
}

Comments

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