Field theory for function fields of plane quartic curves
type: Item
instance of: scholarly article
title: Field theory for function fields of plane quartic curves
zbMATH Open document ID: 0983.11067
author: Kei Miura
author: Hisao Yoshihara
published in: Journal of Algebra
publication date: 2002-04-10T00:00:00Z
review text: Let \(K\) be the rational function field of a smooth plane curve \(C\) of degree \( d\) (\(d\geq 2)\) defined over an algebraic number field \(k\) of characteristic zero. If \(K_m\) denotes a maximal rational subfield of \(K\), the authors of the paper under review answer, in the case where \(C\) is a quartic curve, the following questions. (1) When is the extension \(K/K_m\) Galois? (2) Let \(L\) be the Galois closure of \(K/K_m\). What could we say about \(L\)? (3) What is the Galois group \(\text{Gal}(L/K_m)\)? The characterisation is dependent on the point \(P\), which is the center of the projection of the curve \(C\) to a line \(l\), and of the genus \(g(P)\) of the curve \(\grave{C}\), which corresponds to the field \(L\).
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 1441808
zbMATH Keywords: plane quartic curves
zbMATH Keywords: function field
zbMATH Keywords: Galois group
reviewed by: Jannis A. Antoniadis
MaRDI profile type: Publication
full work available at URL: jabr.1999.8173
OpenAlex ID: W1973592657
cites work: Q3952229
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cites work: Triple coverings of algebraic surfaces according to the Cardano formula
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DOI: 10.1006/JABR.1999.8173
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description: scientific article; zbMATH DE number 1441808