arXiv 0909.46052009-09-28math.AG

杂交玉米品种

On Mixed Brieskorn Variety

Mutsuo Oka

摘要：

令$f_{{\bf a},\{bf b}}({\bf z},\bar{\bf z})=z_1^{a_1+b_1}\bar z_1^{b_1}+...+z_n^{a_n+b_n}\bar z_n^{b_n}$是具有$a_j>0,b_j\ge 0$、$j=1,..., n$的极加权齐次混合多项式，并且令$f_{\bf a}({\bf z})=z_1^{a_1}+...+z_n^{a_n}$是相关联的加权齐次多项式。考虑相应的链接变体$K_{{\bf a},{\bf b}}=f_{{\bf a},{\bf b}}\inv(0)\cap S^{2n-1}$和$K_{\bf a}=f_{\bf a}\inv(0)\cap S^{2n-1}$。Ruas-Seade-Verjovsky \cite{R-S-V}证明了$f_{{\bf a},{\bf b}}$和$f_{\bf a}$的Milnor纤维化是拓扑等价的，混合链环$K_{{\bf a},{\bf b}}$同胚于复链环$K_{\bf a}$ .我们将证明它们是$C^\infty$等价的，并且两个链接是同构的。我们对$ f({\bf z},\bar{\bf z})=z_1^{a_1+b_1}\bar z_1^{b_1}z_2+...+z_{n-1}^{a_{n-1}+b_{n-1}}\bar z_{n-1}^{b_{n-1}}z_n+z_n^{a_n+b_n}\bar z_n^{b_n}$及其相关多项式$ g({\bf z})=z_1^{a_1}z_2+...+ z_{n-1}^{a_{n-1}}z_n+z_n^{a_n}$给出了相同的断言。

英文摘要：

Let $f_{{\bf a},\{bf b}}({\bf z},\bar{\bf z})=z_1^{a_1+b_1}\bar z_1^{b_1}+...+z_n^{a_n+b_n}\bar z_n^{b_n}$ be a polar weighted homogeneous mixed polynomial with $a_j>0,b_j\ge 0$, $j=1,..., n$ and let $f_{\bf a}({\bf z})=z_1^{a_1}+...+z_n^{a_n}$ be the associated weighted homogeneous polynomial. Consider the corresponding link variety $K_{{\bf a},{\bf b}}=f_{{\bf a},{\bf b}}\inv(0)\cap S^{2n-1}$ and $K_{\bf a}=f_{\bf a}\inv(0)\cap S^{2n-1}$. Ruas-Seade-Verjovsky \cite{R-S-V} proved that the Milnor fibrations of $f_{{\bf a},{\bf b}}$ and $f_{\bf a}$ are topologically equivalent and the mixed link $K_{{\bf a},{\bf b}}$ is homeomorphic to the complex link $K_{\bf a}$. We will prove that they are $C^\infty$ equivalent and two links are diffeomorphic. We show the same assertion for $ f({\bf z},\bar{\bf z})=z_1^{a_1+b_1}\bar z_1^{b_1}z_2+...+z_{n-1}^{a_{n-1}+b_{n-1}}\bar z_{n-1}^{b_{n-1}}z_n+z_n^{a_n+b_n}\bar z_n^{b_n}$ and its associated polynomial $ g({\bf z})=z_1^{a_1}z_2+...+ z_{n-1}^{a_{n-1}}z_n+z_n^{a_n}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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