Zariski Pairs on Sextics Ii

We continue to study Zariski pairs in sextics. In this paper, we study Zariski pairs of sextics which are not irreducible. The idea of the construction of Zariski partner sextic for reducible cases is quit different from the irreducible case. It is crucial to take the geometry of the components and their mutual intersection data into account. When there is a line component, flex geometry (i.e., linear geometry) is concerned to the geometry of sextics of torus type and non-torus type. When there is no linear components, the geometry is more difficult to distinguish sextics of torus type. For this reason, we introduce the notion of conical flexes. We have observed in [9] that the case ρ(C, 5) = 6 is critical in the sense that the Alexander polynomial ∆C(t) can be either trivial or non-trivial for sextics. If ρ(C, 5) > 6 (resp. ρ(C, 5) < 6), the Alexander polynomial is not trivial (resp. trivial) ([9]). For the definition of ρ(C, 5)invariant, see [9]. Thus we concentrate ourselves in this paper the case ρ(C, 5) = 6. In [10], we have classified the possible configurations for reducible sextics of torus type. In particular, the configurations with ρ(C, 5) = 6 are given as in Theorem 1 below. Hereafter we use the same notations as [9] for denoting component types. For example, C = B1 +B5 implies that C has a linear component B1 and a quintic component B5. We denote the configuration of the singularities of C by Σ(C).