Linear automorphisms of smooth hypersurfaces giving Galois points
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 617-635
https://doi.org/10.4134/BKMS.b200428
Published online March 5, 2021
Printed May 31, 2021
Taro Hayashi
Kindai University
Abstract : Let $X$ be a smooth hypersurface $X$ of degree $d\geq4$ in a projective space $\mathbb P^{n+1}$. We consider a projection of $X$ from $p\in\mathbb P^{n+1}$ to a plane $H\cong\mathbb P^n$. This projection induces an extension of function fields $\mathbb C(X)/\mathbb C(\mathbb P^n)$. The point $p$ is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for $X$ to have Galois points by using linear automorphisms.
Keywords : Smooth hypersurface, automorphism, Galois point, Galois extension
MSC numbers : Primary 14J70; Secondary 12F10
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