Abstract
A simple sextic is a reduced complex projective plane curve of degree 6 with only simple singularities. We introduce a notion of Z-splitting curves for the double covering of the projective plane branching along a simple sextic, and investigate lattice Zariski k-ples of simple sextics by Z-splitting curves. We define specialization of lattice types, and classify all lattice types of Z-splitting curves of degree less than or equal to 3 up to specializations.
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