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

  • Alice Cuzzucoli Department of Mathematics, University of Warwick, Coventry, CV4 7AL, Warwickshire, England
  • Riccardo Moschetti Department of Mathematics and Natural Sciences, University of Stavanger, NO-4036 Stavanger, Norway
  • Maiko Serizawa School of Mathematics and Statistics, University of Sheffield, Western Bank, Sheffield, S10 2TN, South Yorkshire, England
Keywords: Monodromy, Projections, Uniform points, Focal points, Filling families


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.