I‑AIMS Institute for Artificial Intelligence
and Mathematical Sciences
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Reduction of superelliptic Riemann surfaces

Tanush Shaska

I-AIMS paper 2020-1 · Published in Contemp. Math. 776 (2022), 227–247 · 2022

For a superelliptic curve 𝒳, defined over ℚ, let 𝔭 denote the corresponding moduli point in the weighted moduli space. We describe a method how to determine a minimal integral model of 𝒳 such that: i) the corresponding moduli point 𝔭 has minimal weighted height, ii) the equation of the curve has minimal coefficients. Part i) is accomplished by reduction of the moduli point which is equivalent with obtaining a representation of the moduli point 𝔭 with minimal weighted height, and part ii) by the classical reduction of the binary forms.

MSC classes: 14G40

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References

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