## Journal of the Mathematical Society of Japan

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

### Galois points on quartic surfaces

#### 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 $k\left(S\right)/k\left(H\right)$. 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

**Keywords**

Quartic surface Projective transformation Galois point Elliptic surface

#### 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