Galois lines for normal elliptic space curves, II

Details Galois lines for normal elliptic space curves, II Galois lines for normal elliptic space curves, II

2010-04-28

arxiv.org/abs/1004.4962v1

Mathematics

Algebraic Geometry

For Galois points or Galois lines, please visit my web page: http://mathweb.sc.niigata-u.ac.jp/~yosihara/openquestion.html

Scientific paper

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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