Monodromy of projections of hypersurfaces

2020/02/22 by Cifani, Maria Gioia, Cuzzucoli, Alice, Moschetti, Riccardo · 1 citation
#14H30 #14H50 #14J10 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.09698

Abstract

Let X be an irreducible, reduced complex projective hypersurface of degree d. A point P not contained in X is called uniform if the monodromy group of the projection of X from P is isomorphic to the symmetric group S_d. We prove that the locus of non--uniform points is finite when X is smooth or a general projection of a smooth variety. In general, it is contained in a finite union of linear spaces of codimension at least 2, except possibly for a special class of hypersurfaces with singular locus linear in codimension 1. Moreover, we generalise a result of Fukasawa and Takahashi on the finiteness of Galois points.

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