Equations for generalized superelliptic Riemann surfaces

Rubén A. Hidalgo, Saúl Quispe, Tanush Shaska

I-AIMS preprint 2024-01 · 2024

Let 𝒳 be a closed Riemann surface, τ ∈ G = Aut(𝒳) be a conformal automorphism of order n ≥ 2 such that 𝒳/⟨τ⟩ has genus zero, and N be the normalizer of ⟨τ⟩ in G. In this paper, if ⟨τ⟩ is central in N, we determine parametric equations of all curves 𝒳 and their corresponding genus.

MSC classes: Primary 14H37; Secondary 30F10, 14H45

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