Triple coverings of the projective plane branched along quintic curves (Q533329)

Let \(S\) be a normal complex surface and let \(\pi: S\to {\mathbb P}^2({\mathbb C})\) be a triple covering, namely a finite degree 3 map. Assume in addition that the branch locus of \(\pi\) (considered with the reduced structure) is the union of a quartic \(Q\) and a line \(l\), and that \(\pi\) is simply ramified over a general point of \(Q\) and totally ramified over any point of \(l\). The main result of the paper is that, in the above situation, the surface \(S\) is a cubic surface of \({\mathbb P}^3\) and the morphism \(\pi\) is induced by projection from a point \(p\in {\mathbb P}^3\setminus S\).