Non Uniform Projections of Surfaces in P3 Alice Cuzzucoli - Riccardo Moschetti - Maiko Serizawa

In this paper we study the monodromy groups of projections of smooth irreducible surfaces in P3 from points. Our particular interest lies in finding whether the monodromy group of a projection πL of a surface from a point L is the whole symmetric group or not. In the former case, we call L uniform, and in the latter case, not uniform. The very same terminology is also used for the whole projection, calling πL uniform if and only if the monodromy group M(πL) is the whole symmetric group. Much work has been done in the literature for the case of curves to determine which groups can arise as the monodromy group of some projection. The papers [GN95], [GM98] and [GS07] show that if C is a general curve of genus greater than 3, then the monodromy group of a projection C→P1 is either the whole symmetric group or the alternating group. A general curve of degree d and genus g admits a covering with symmetric monodromy group