I‑AIMS Institute for Artificial Intelligence
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Deciding Superellipticity and Computing Superelliptic Normal Forms

Tanush Shaska

I-AIMS preprint sh-92 · 2026

Let 𝒮_(g,n) ⊂ ℳ_g be the locus of curves of genus g ≥ 2 admitting a model yⁿ = h(x) with h separable; such curves C have a cyclic group Cₙ ≤ Aut(C) of order n with C/Cₙ ≅ ℙ¹. We give an algorithm which, given an absolutely irreducible plane model F(x, y) = 0 of a curve C over a field k₀ of characteristic zero, decides for which n the curve lies in 𝒮_(g,n) and returns a model yⁿ = h(x) together with the birational transformation to it.

MSC classes: Primary 14H37, 14Q05; Secondary 14H30, 14H55, 11G30

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