Galois lines for normal elliptic space curves, II

preprint2010arXivOpen access

Abstract

For each linearly normal elliptic curve CC in P3\mathbb P^3, we determine Galois lines and their arrangement. The results are as follows: the curve CC has just six V4V_4-lines and in case j(C)=1j(C)=1, it has eight Z4Z_4-lines in addition. The V4V_4-lines form the edges of a tetrahedron, in case j(C)=1j(C)=1, for each vertex of the tetrahedron, there exist just two Z4Z_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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