## Journal of the Mathematical Society of Japan

### Galois points on quartic surfaces

Hisao YOSHIHARA

#### Abstract

Let $S$ be a smooth hypersurface in the projective three space and consider a projection of $S$ from $P\in S$ to a plane $H$. This projection induces an extension of fields $k(S)/k(H)$. The point $P$ is called a Galois point if the extension is Galois. We study structures of quartic surfaces focusing on Galois points. We will show that the number of the Galois points is zero, one, two, four or eight and the existence of some rule of distribution of the Galois points.

#### Article information

Source
J. Math. Soc. Japan, Volume 53, Number 3 (2001), 731-743.

Dates
First available in Project Euclid: 9 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213023732

Digital Object Identifier
doi:10.2969/jmsj/05330731

Mathematical Reviews number (MathSciNet)
MR1828978

Zentralblatt MATH identifier
1067.14510

Subjects
Primary: 14J70: Hypersurfaces
Secondary: 14J27: Elliptic surfaces 14J28: $K3$ surfaces and Enriques surfaces

#### Citation

YOSHIHARA, Hisao. Galois points on quartic surfaces. J. Math. Soc. Japan 53 (2001), no. 3, 731--743. doi:10.2969/jmsj/05330731. https://projecteuclid.org/euclid.jmsj/1213023732