Fundamental groups of complements to singular plane curves
Fundamental groups of complements to singular plane curves
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奇异平面曲线补集的基本群
DOI：
10.1353/ajm.1997.0006
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发表时间：
1997
影响因子：
1.7
通讯作者：
I. Shimada
中科院分区：
文献类型：
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作者：
I. Shimada
本文将复射影空间中关于超曲面补的基本群的经典的Zagliki超平面截口定理推广到加权齐次情形。利用这个结果，我们研究了射影平面曲线的补曲线的基本群在射影平面被另一个射影平面覆盖的情况下如何变化。我们还给出了一个例子，平面曲线的补有nonabel和有限的基本群。这种曲线的例子很少。利用加权Zerkiki超平面截口定理，我们可以确定这些有限非交换群的群结构。0.导论.本文的第一部分给出并证明了复射影空间中超曲面补元基本群上的加权齐次形式的Zapriki超平面截口定理，并讨论了它在射影平面曲线补元基本群上的一些直接应用。在第二部分中，我们研究了一类奇异平面曲线C（q9k）9，它是Zenkiki的三个尖点四次曲线的推广，并利用第一部分的主要结果计算了其基本群^（P2 \ C（q9k））.这个群是有限的，非阿贝尔群。让jci，。。9xn是具有权重的变量
The classical hyperplane section theorem of Zariski about the fundamental groups of the complements to hypersurfaces in the complex projective space is generalized to the weighted homogeneous case. Using this result, we study how the fundamental group of the complement to a projective plane curve changes under covering of the projective plane by another projective plane. We also give an example of plane curves whose complements have nonabelian and finite fundamental groups. Few examples of such curves have been known. By the weighted Zariski's hyperplane section theorem, we can determine the group structure of these finite nonabelian groups. 0. Introduction. In the first part of this paper, we formulate and prove a weighted homogeneous version of Zariski's hyperplane section theorem on the fundamental groups of the complements to hypersurfaces in a complex projective space, and discuss some direct applications to the fundamental groups of com plements to projective plane curves. In the second part, we investigate a certain singular plane curve C(q9 k)9 which is a generalization of Zariski's three cuspidal quartics, and calculate the fundamental group ^(P2 \ C(q9k)) using the main result of the first part. This group turns out to be finite and nonabelian. Let jci, ... 9xn be variables with weights
DOI：
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发表时间：
2005
期刊：
J.Math.Soc.Japan Vol.57,No 1
影响因子：
--
作者：
Eyral C.;Oka M.
通讯作者：
Oka M.