Nihonkai Mathematical Journal

A note on Galois embedding and its application to $\mathbb P^n$

Hisao Yoshihara

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Abstract

We show a condition that a Galois covering $\pi : V \longrightarrow \mathbb P^n$ is induced by a Galois embedding. Then we consider the Galois embedding for $\mathbb P^n$. If the Galois group $G$ is abelian, then $G \cong \bigoplus\limits^{n} Z_d$ and the projection $\pi$ can be expressed as $\pi(X_0:X_1: \cdots :X_n)=({X_0}^d:{X_1}^d:\cdots:{X_n}^d)$.

Note

This work is based on research 15K04813 supported by Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science.

Article information

Source
Nihonkai Math. J., Volume 28, Number 2 (2017), 99-104.

Dates
Received: 22 September 2016
Revised: 13 May 2017
First available in Project Euclid: 26 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1524708084

Mathematical Reviews number (MathSciNet)
MR3794318

Zentralblatt MATH identifier
06873762

Subjects
Primary: 14N05: Projective techniques [See also 51N35] 14N10: Enumerative problems (combinatorial problems)
Secondary: 14J99: None of the above, but in this section

Keywords
Galois embedding Galois group projective space

Citation

Yoshihara, Hisao. A note on Galois embedding and its application to $\mathbb P^n$. Nihonkai Math. J. 28 (2017), no. 2, 99--104. https://projecteuclid.org/euclid.nihmj/1524708084


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