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arxiv: 1004.4962 · v1 · pith:CYYLB65Rnew · submitted 2010-04-28 · 🧮 math.AG

Galois lines for normal elliptic space curves, II

classification 🧮 math.AG
keywords linescurvegaloiscaseellipticjustnormaltetrahedron
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For each linearly normal elliptic curve $C$ in $\mathbb P^3$, we determine Galois lines and their arrangement. The results are as follows: the curve $C$ has just six $V_4$-lines and in case $j(C)=1$, it has eight $Z_4$-lines in addition. The $V_4$-lines form the edges of a tetrahedron, in case $j(C)=1$, for each vertex of the tetrahedron, there exist just two $Z_4$-lines passing through it. We obtain as a corollary that each plane quartic curve of genus one does not have more than one Galois point.

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