English

Galois lines for normal elliptic space curves, II

Algebraic Geometry 2015-03-17 v1

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.

Keywords

Cite

@article{arxiv.1004.4962,
  title  = {Galois lines for normal elliptic space curves, II},
  author = {Hisao Yoshihara},
  journal= {arXiv preprint arXiv:1004.4962},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-21T15:15:46.045Z