Dihedral coverings branched along maximizing sextics (Q1364375): Difference between revisions

Let \(C\) be a maximizing sextic. We study a \({\mathcal D}_{2p}\) (\(p\): odd prime) covering of \(\mathbb{P}^2\) branched along \(C\). Suppose that \(C\) is irreducible and has at least one triple point. Then, for \(p\geq 5\), there is no \({\mathcal D}_{2p}\) covering branched along \(C\). For \(p=3\), we give a sufficient condition for \(C\) to be the branch locus of a \({\mathcal D}_6\) covering. Several examples of such \(C\) are given.