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March 2008 The genera of Galois closure curves for plane quartic curves
S. Watanabe
Hiroshima Math. J. 38(1): 125-134 (March 2008). DOI: 10.32917/hmj/1207580347

Abstract

Let $C$ be a smooth plane quartic curve defined over a field $k$ and $k(C)$ the rational function field of $C$. Let $\pi_P$ be the projection from $C$ to a line $\ell$ with a center $P\in C$. Then $\pi_P$ induces an extension of fields; $k(C)/k(\ell)$. Let $\widetilde C$ be a nonsingular model of the Galois closure of the extension, which we call the Galois closure curve of $k(C)/k(\ell)$. We give an answer to the problem for the genus of the Galois closure curve of quartic curve.

Citation

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S. Watanabe. "The genera of Galois closure curves for plane quartic curves." Hiroshima Math. J. 38 (1) 125 - 134, March 2008. https://doi.org/10.32917/hmj/1207580347

Information

Published: March 2008
First available in Project Euclid: 7 April 2008

zbMATH: 1142.14021
MathSciNet: MR2397382
Digital Object Identifier: 10.32917/hmj/1207580347

Subjects:
Primary: 14H05, 14H45

Rights: Copyright © 2008 Hiroshima University, Mathematics Program

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Vol.38 • No. 1 • March 2008
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