The genera of Galois closure curves for plane quartic curves

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概要

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• 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 \cite{my}.

著者

• Watanabe Shingo

  Graduate School Of Science And Technology Niigata University Niigata 950-2181 Japan

関連論文

• The genera of Galois closure curves for plane quartic curves

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