Knotting of algebraic curves in complex surfaces

Details Knotting of algebraic curves in complex surfaces Knotting of algebraic curves in complex surfaces

2000-11-27

arxiv.org/abs/math/0011227v1

Mathematics

Geometric Topology

12 pages, 4 figures, includes gokova.cls

Scientific paper

A non-singular connected algebraic curve $A$ in a simply connected algebraic surface $X$ can be knotted so that its homology class and the fundamental group of its complement in $X$ is preserved, provided $A$ is sufficiently complex (not too ``rigid''). For example, it is true if $A$ admits a degeneration to an irreducible curve $A_0$ having a unique singularity of the type $X_9$ (a non-degenerate quadriple point), or more complicated one, and $A.A>16$. This generalizes the previous result of the author which concerns the curves in $CP^2$ of degree $d>4$ (the old preprint is included as a part of the current one).

Affiliated with

Also associated with

No associations

Rating

Knotting of algebraic curves in complex surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Knotting of algebraic curves in complex surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Knotting of algebraic curves in complex surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-217534