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Galois lines for normal elliptic space curves, II · arXivDesk

1004.4962Apr 28, 2010For Galois points or Galois lines, please visit my web page: http://mathweb.sc.niigata-u.ac.jp/~yosihara/openquestion.html

Galois lines for normal elliptic space curves, II

Hisao Yoshihara

Algebraic Geometry

Abstract

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 $V_4$

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-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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