Geometry of bisections of elliptic surfaces and Zariski $N$-plets II
Geometry of bisections of elliptic surfaces and Zariski $N$-plets II
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椭圆曲面平分几何和 Zariski $N$-plets II
DOI：
10.1016/j.topol.2017.09.003
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发表时间：
2017
影响因子：
0.6
通讯作者：
S.Bannai and H.Tokunaga
中科院分区：
文献类型：
--
作者：
S.Bannai;B.Guerville - Balle; T.Shirane and H.Tokunaga;S.Bannai and H.Tokunaga
本文考虑不可约分量为不可约四次光滑二次曲线的Zariski N-Plets。更确切地说，我们给出了2N+4次Zariski N+1-Plets的例子，其不可约分量是具有2个结点和N个光滑二次曲线的不可约四次曲线。我们构造了这样的例子作为我们对某些有理椭圆曲面平分几何研究的一个应用。此外，通过考虑N=2的情况，并结合已有的结果，给出了一个新的8次约化平面曲线的Zariski 5-Plet。
In this article, we consider Zariski N-plets whose irreducible components are an irreducible quartic and smooth conics. More precisely we give examples of Zariski N+ 1-plets of degree 2 N+ 4 whose irreducible components are an irreducible quartic curve with 2 nodes and N smooth conics. We construct such examples as an application of our study of the geometry of bisections of certain rational elliptic surfaces. Moreover, by considering the case of N= 2 and combining with known results, a new Zariski 5-plet for reduced plane curves of degree 8 is given.