Knotting of Algebraic Curves in CP2
classification
🧮 math.GT
math.AG
keywords
algebraicconstructcurvecurvesabelianambientanswerclass
read the original abstract
I 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.