Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics

Details Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics

2009-03-19

arxiv.org/abs/0903.3308v2

Mathematics

Algebraic Geometry

40 pages, remarks are added, an example in the last section is removed, typos are corrected

Scientific paper

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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