Some examples of Zariski pairs arising from certain elliptic K3 surfaces. II: Degtyarev's conjecture
[For part I of this paper see Math. Z. 227, No. 3, 465-477 (1998; Zbl 0923.14012).] Two projective plane curves \(C_1, C_2\) form a Zariski pair if they have the same degree and same type of singularity but with non-isomorphic complements in the plane. An affirmative answer to Degtyarev's conjecture would imply that there is no certain Zariski pair of degree 6. Here the author among other things, disproves the conjecture by producing counterexamples. In general, it is very difficult to construct such examples due to subtlety of the difference of \(C_1, C_2\).
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