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.

中文翻译：

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超曲面投影的单向性

令X是度数为d的不可约、约简复数射影超曲面。如果X从P的投影的单向群与对称群\(S_d\)同构，则不包含在X 中的点P被称为一致的。我们证明了当X是光滑的或光滑类的一般投影时，非均匀点的轨迹是有限的。一般而言，它包含在至少为 2 的余维线性空间的有限并集中，除了在余维 1 中具有奇异轨迹线性的一类特殊超曲面。此外，我们推广了 Fukasawa 和 Takahashi 关于 Galois 的有限性的结果点。