Triangular curves and cyclotomic Zariski tuples
Triangular curves and cyclotomic Zariski tuples
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三角曲线和分圆 Zariski 元组
DOI：
10.1007/s13348-019-00269-y
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发表时间：
2019
影响因子：
1.1
通讯作者：
J. Mart'in
中科院分区：
文献类型：
--
作者：
Enrique Artal Bartolo;J. Cogolludo;J. Mart'in
本文的目的是证明在数域上共轭投影曲线的无穷族，它们的补具有相同的阿贝尔基本群，但是非同胚的。特别地，我们找到了由单位根参数化到复共轭的zariski元组。因此，对于任何分模，，我们在相应的分环场中找到具有系数的算术zariski元组。这些曲线都有阿贝尔基本群，用一个连接不变量来区分它们。
The purpose of this paper is to exhibit infinite families of conjugate projective curves in a number field whose complement have the same abelian fundamental group, but are non-homeomorphic. In particular, for anywe find Zariski-tuples parametrized by thed-roots of unity up to complex conjugation. As a consequence, for any divisormofd,, we find arithmetic Zariski-tuples with coefficients in the corresponding cyclotomic field. These curves have abelian fundamental group and they are distinguished using a linking invariant.