| Summary: | The uniqueness of the hyperelliptic involution is well known in the theory
of Riemann surfaces. More precisely, we know that if X is a hyperelliptic
compact Riemann surface, there is a unique automorphism τ of order 2 such
that X/〈τ〉 ≅ ℙ¹ . We wish to generalize the situation slightly. We say X
is a prime Galois covering of ℙ¹ if there exists an automorphism τ of (odd)
prime order p such that X/〈T〉 ≅ ℙ¹. This leads us to ask the question:
When is this automorphism τ unique?
We begin by building the necessary background to understand prime
Galois coverings of ℙ¹. We then prove a theorem due to Gonzlez-Diez that
answers our question about uniqueness. The proof given here follows his
proof (given in [G-D]) quite closely, though we elaborate and modify certain
details to make it more self contained. === Science, Faculty of === Mathematics, Department of === Graduate
|
|---|
