论文标题
在$μ$ -zariski上
On $ μ$-Zariski pairs of links
论文作者
论文摘要
自$ \ mathbb p^2 $中的Zariski Pairs的概念以来，自Zariski \ cite \ cite {Zariski}的先驱论文和进一步开发以来，我们引用了\ cite {bartolo}的参考。 Such a pair is canonically produced from a Zariski (or a weak Zariski ) pair of curves $C=\{f(x,y,z)=0\}$ and $C'=\{g(x,y,z)=0\}$ of degree $d$ by simply adding a monomial $z^{d+m}$ to $f$ and $g$ so that the corresponding affine hypersurfaces起源有孤立的奇异性。它们具有相同的ZETA函数和相同的Milnor编号（\ cite {几乎}）。我们提供了具有相同$μ^*$序列和相同ZETA功能的Zariski对的新示例，但两个函数属于$μ$ -Constant Strata的不同连接组件（theorem \ ref Ref {Mu-Zariski}）。两个链接3倍不是差异形态，它们是由第一个同源性区分的，这意味着其单粒的约旦形式是不同的（theorem \ ref {main2}）。我们从弱Zariski对射击曲线开始，构建新的Zariski对表面，这些表面具有3倍的非呈差异链路。我们还证明，由Zariski对构建的高表面对给出了一个差异链接（定理\ ref {main3}）。
The notion of Zariski pairs for projective curves in $\mathbb P^2$ is known since the pioneer paper of Zariski \cite{Zariski} and for further development, we refer the reference in \cite{Bartolo}.In this paper, we introduce a notion of Zariski pair of links in the class of isolated hypersurface singularities. Such a pair is canonically produced from a Zariski (or a weak Zariski ) pair of curves $C=\{f(x,y,z)=0\}$ and $C'=\{g(x,y,z)=0\}$ of degree $d$ by simply adding a monomial $z^{d+m}$ to $f$ and $g$ so that the corresponding affine hypersurfaces have isolated singularities at the origin. They have a same zeta function and a same Milnor number (\cite{Almost}). We give new examples of Zariski pairs which have the same $μ^*$ sequence and a same zeta function but two functions belong to different connected components of $μ$-constant strata (Theorem \ref{mu-zariski}). Two link 3-folds are not diffeomorphic and they are distinguished by the first homology which implies the Jordan form of their monodromies are different (Theorem \ref{main2}). We start from weak Zariski pairs of projective curves to construct new Zariski pairs of surfaces which have non-diffeomorphic link 3-folds. We also prove that hypersurface pair constructed from a Zariski pair give a diffeomorphic links (Theorem \ref{main3}).
