Abstract
In this article, we make use of geometry of sections of elliptic surfaces and elementary arithmetic on the Mordell-Weil group in order to study existence problem of dihedral covers with given reduced curves as the branch loci. As an application, we give some examples of Zariski pairs $(B_1, B_2)$ for “conic-line arrangements” satisfying the following conditions:
(i) $\deg B_1 = \deg B_2 = 7$.
(ii) Irreducible components of $B_i$ $(i = 1, 2)$ are lines and conics.
(iii) Singularities of $B_i$ ($i = 1, 2$) are nodes, tacnodes and ordinary triple points.
Citation
Hiro-o TOKUNAGA. "Sections of elliptic surfaces and Zariski pairs for conic-line arrangements via dihedral covers." J. Math. Soc. Japan 66 (2) 613 - 640, April, 2014. https://doi.org/10.2969/jmsj/06620613
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