Galois Lines for Normal Elliptic Space Curves

Abstract

Let C be a curve, and l and l0 be lines in the projective three space ℙ3. Consider a projection πl: ℙ3 ⋯ → l0 with center l, where l ⋂ l0= ∅. Restricting πl to C, we obtain a morphism πl|C : C → l0 and an extension of fields (πl|C)* : k(l0) ↪ k(C). If this extension is Galois, then l is said to be a Galois line. We study the defining equations, automorphisms and the Galois lines for quartic curves, and give some applications to the theory of plane quartic curves.