Non uniform projections of surfaces in $\P^3$
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.
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