Papers › Integral differential forms for superelliptic curves
Integral differential forms for superelliptic curves
Sabrina Kunzweiler, Stefan Wewers
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Given a superelliptic curve Y_K : yⁿ = f(x) over a local field K, we describe the theoretical background and an implementation of a new algorithm for computing the 𝒪_K-lattice of integral differential forms on Y_K. We build on the results of Obus and the second author, which describe arbitrary regular models of the projective line using only valuations. One novelty of our approach is that we construct an 𝒪_K-model of Y_K with only rational singularities, but which may not be regular.
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