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arXiv · 1405.4556

Equations for superelliptic curves over their minimal field of definition

Lubjana Beshaj·Fred Thompson
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Abstract

Let $\mathcal X_g$ be a genus $g\geq 2$ superelliptic curve, $F$ its field of moduli, and $K$ the minimal field of definition. In this short note we construct an equation of the curve $\mathcal X_g$ over its minimal field of definition $K$ when $\mathcal X_g$ has extra automorphisms. We make use of the dihedral invariants of superelliptic curves as defined by Shaska in [6] and results on the automorphism groups of superelliptic curves as in [10].

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Lubjana Beshaj, Fred Thompson. 2014-07-23. Equations for superelliptic curves over their minimal field of definition. https://arxiv.org/abs/1405.4556

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