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

Abstract

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.

11 pages, no figures. This paper is a result of the work carried out at PRAGMATIC 2016 Research School. Minor changes and journal references added