On the Fundamental Group of the Complement of a Reducible Curve in P2
On the Fundamental Group of the Complement of a Reducible Curve in P2
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论P2中可约曲线补集的基本群
DOI：
10.1112/jlms/s2-12.2.239
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发表时间：
1976
影响因子：
1.2
通讯作者：
M. Oka
中科院分区：
文献类型：
--
作者：
M. Oka
设C=C 1 u C 2 u.U，C，Bean P2中的代数曲线，使得它的不可约分支{C，}处于一般位置，即对于每个相互不同的i，j(i#j)和C，n C，nCk=0，C{和Cj横向相交。我们如何用Tt^P2-Cj){j=1，2，…，r来确定基本群^(P2-C)？Zariski的猜想说，如果每个不可约分支Cj只有普通的双点作为奇点，则Tt^P2-C)应该是阿贝尔的[4]。我们的结果部分地回答了这个问题。
Let C= C 1 u C 2 u... u C, bean algebraic curve in P2 such that its irreducible components {C,} are in general position ie C {and Cj meet transversely for each i, j (i# j) and C, n C, n Ck= 0 for each mutually distinct i, j and k. How can we decide the fundamental group^(P 2-C) in the words of TT^ P2-Cj){j= 1, 2,..., r)? Zariski's conjecture says that TT^ P2—C) should be abelian if each irreducible component Cj has only ordinary double points as singularities [4]. Our results are partial answers to this question.