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