Integral differential forms for superelliptic curves

Kunzweiler, Sabrina; Wewers, Stefan

doi:10.1090/mcom/4115

Integral differential forms for superelliptic curves
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by Sabrina Kunzweiler and Stefan Wewers;

Math. Comp.

DOI: https://doi.org/10.1090/mcom/4115

Published electronically: June 24, 2025

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Abstract:

Given a superelliptic curve $Y_K:\; y^n=f(x)$ over a local field $K$, we describe the theoretical background and an implementation of a new algorithm for computing the $\mathfrak {o}_K$-lattice of integral differential forms on $Y_K$. We build on the results of Obus and Wewers [J. Algebraic Geom. 29 (2020), pp. 691–728] who describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an $\mathfrak {o}_K$-model of $Y_K$ with only rational singularities, but which may not be regular.

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Mathematics of Computation

Integral differential forms for superelliptic curves
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Abstract: