Knotting of Algebraic Curves in CP2
Geometric Topology
2007-05-23 v3 Algebraic Geometry
Abstract
I construct "fake algebraic curves" in . More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces 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 . This gives an answer to Problem 4.110 of Kirby's list.
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