Triple coverings of the projective plane branched along quintic curves

Abstract

In this article, we characterize triple coverings over the projective plane $\mathbb{P}^{2}$ branched along quintic curves with some conditions. The main result is that such triple coverings are induced by projections $\mathbb{P}^{3} \dashrightarrow \mathbb{P}^{2}$ from certain points.