A note on non-uniform points for projections of hypersurfaces

TL;DR

This paper investigates the properties of points on complex projective hypersurfaces that affect the monodromy of their projections, extending previous results to include points on the hypersurface itself.

Contribution

It extends and refines earlier results on the finiteness of non-uniform points for hypersurface projections, now including points on the hypersurface.

Findings

Finiteness of the locus of non-uniform points is established.

Results are extended to include points contained in the hypersurface.

Improved understanding of projection monodromy for complex hypersurfaces.

Abstract

Let X be an irreducible, reduced complex projective hypersurface of degree d. A uniform point for X is a point P such that the projection of X from P has maximal monodromy. We extend and improve some results concerning the finiteness of the locus of non-uniform points for projections of hypersurfaces obtained by the authors and Cuzzucoli only for P not contained in X.