Plane curves whose singular points are cusps and triple coverings of \(\mathbb{P}^2\)
Let \(C\) be an algebraic plane curve in the complex projective plane \(\mathbb{P}^2\); assume that \(C\) has degree \(d\in 3\mathbb{Z}\) and, furthermore, that its only singular points are unibranched double or triple points. The author finds an inequality relating some invariants of the singular points of \(C\), obtained from their multiplicities and maximal contacts, and the degree d of the curve. The proof uses triple coverings of \(\mathbb{P}^2\) branched along \(C\) and some of them give examples of minimal surfaces of general type.
scientific article; zbMATH DE number 4163055