2021
DOI: 10.48550/arxiv.2101.04797
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Linear automorphisms of smooth hypersurfaces giving Galois points

Taro Hayashi

Abstract: Let X be a smooth hypersurface X of degree d ≥ 4 in a projective space P n+1 . We consider a projection of X from p ∈ P n+1 to a plane H ∼ = P n . This projection induces an extension of function fields C(X)/C(P n ). The point p is called a Galois point if the extension is Galois. In this paper, we will give a necessary and sufficient conditions for X to have Galois points by using linear automorphisms.

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