Knotting of algebraic curves in complex surfaces

Sergey Finashin

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Knotting of algebraic curves in complex surfaces

Sergey Finashin

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Abstract

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).

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BibTeX RIS

Sergey Finashin. 2000-11-27. Knotting of algebraic curves in complex surfaces. https://arxiv.org/abs/math/0011227

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