Sections of elliptic surfaces and Zariski pairs for conic-line arrangements via dihedral covers

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 (B1, B2) 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.