Non Uniform Projections of Surfaces in P3\mathbb{P}^3

Consider the projection of a smooth irreducible surface in $\mathbb{P}^3$ from a point. The uniform position principle implies that the monodromy group of such a projection from a general point in $\mathbb{P}^3$ is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we prove that the locus of non-uniform points of $\mathbb{P}^3$ is at most finite.Comment: 11 pages, no figures. This paper is a result of the work carried out at PRAGMATIC 2016 Research School. Minor changes and journal references adde

Non uniform projections of surfaces in ¶3\P^3

Consider the projection of a smooth irreducible surface in $\P^3$ from a point.The uniform position principle implies that the monodromy group of such a projection from a general point in $\P^3$ is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we proved that the locus of non-uniform points of $\P^3$ is at most finite