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

Alice Cuzzucoli; Riccardo Moschetti; Maiko Serizawa

doi:10.4418/2017.72.2.8

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arXiv · 1705.10135

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

Alice Cuzzucoli·Riccardo Moschetti·Maiko Serizawa

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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.

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Alice Cuzzucoli, Riccardo Moschetti, Maiko Serizawa. 2017-05-29. Non Uniform Projections of Surfaces in $\mathbb{P}^3$. https://doi.org/10.4418/2017.72.2.8

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