The Galois group of a projection of a Hermitian curve. (English) Zbl 1140.14304

Homma, Masaaki

Int. J. Algebra 1, No. 9-12, 563-585 (2007).

Summary: For a Hermitian curve \(H\) in projective plane \(\mathbb P^2\) and an arbitrary point \(P\) of \(\mathbb P^2\), we find out the Galois group of the projection \(H\to\mathbb P^1\) with center \(P\). To achieve this aim, we discuss the Galois group of an equation and that of a finite separable morphism between curves in slightly more general context. Moreover, we compute the genus of the so-called Galois-closure curve \(\widetilde{H}_P\).

MSC:

14H45	Special algebraic curves and curves of low genus
14H50	Plane and space curves
14H25	Arithmetic ground fields for curves