Yoshihara, Hisao A note on Galois embedding and its application to \(\mathbb{P}^n\). (English) Zbl 1391.14107 Nihonkai Math. J. 28, No. 2, 99-104 (2017). Summary: We show a condition that a Galois covering \(\pi:V\to\mathbb{P}^n\) 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 \(\pi(X_0:X_1:\cdots:X_n)=(X_0^d:X_1^d:\cdots:X_n^d)\). MSC: 14N05 Projective techniques in algebraic geometry 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14J99 Surfaces and higher-dimensional varieties Keywords:Galois embedding; Galois group; projective space × Cite Format Result Cite Review PDF Full Text: Euclid References: [1] I. Dolgachev, Reflection group in algebraic geometry, Bull. Amer. Math. Soc. 45 (2008), 1-60. · Zbl 1278.14001 · doi:10.1090/S0273-0979-07-01190-1 [2] J. Harris, Galois groups of enumerative problems, Duke Math. J. 46 (1979), 685-724. · Zbl 0433.14040 [3] M. Namba, Branched coverings and algebraic functions, Pitman Research Notes in Mathematics Series 161. · Zbl 0706.14017 [4] H. Yoshihara, Galois points for plane rational curves, Far East J. Math. Sci. 25 (2007), 273-284. · Zbl 1132.14309 [5] H. Yoshihara, Galois embedding of algebraic variety and its application to abelian surface, Rend. Semin. Mat. Univ. Padova 117 (2007), 69-85. · Zbl 1136.14041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.