复杂曲面中代数曲线的纽结
Knotting of algebraic curves in complex surfaces
摘要：
单连通代数曲面$X$中的非奇异连通代数曲线$A$可以打结，使得它的同调类和它在$X$中的补的基本群被保留，只要$A$足够复杂（不太"刚性“）。例如，如果$A$允许退化到不可约曲线$A_0$，该不可约曲线$A_0$具有唯一的$X_9$类型奇点（非退化四重点）或更复杂的奇点，以及$A.A>16$。这推广了作者以前关于$d>4$阶的$CP^2$中曲线的结果（旧的预印本作为当前预印本的一部分被包括在内）。
英文摘要：
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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