Field of definition and Galois orbits for the Macbeath-Hurwitz curves
type: Item
instance of: scholarly article
title: Field of definition and Galois orbits for the Macbeath-Hurwitz curves
zbMATH Open document ID: 0972.14023
published in: Archiv der Mathematik
publication date: 2001-07-04T00:00:00Z
review text: Hurwitz curves of genus \(g \geq 2\) are those for which the automorphisms group has the maximal order, that is \(84(g-1)\). In this paper the author considers an infinite series of Hurwitz curves, the Macbeath-Hurwitz curves. The main result asserts that a minimal field of definition for these curves are either \(\mathbb Q\) or \({\mathbb Q}(\zeta_{7}+\zeta_{7}^{-1})\), where \(\zeta_{7}=\exp(2 \pi i/7)\).
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 1484680
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: Hurwitz groups
zbMATH Keywords: algebraic curves
zbMATH Keywords: Macbeath-Hurwitz curves
zbMATH Keywords: field of definition
author: Manfred Streit
reviewed by: Rubén A. Hidalgo
MaRDI profile type: Publication
full work available at URL: s000130050453
OpenAlex ID: W2091006162
DOI: 10.1007/S000130050453
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description: scientific article; zbMATH DE number 1484680