Sabrina Kunzweiler

Models of Superelliptic Curves and Integral Differentials

I will present an algorithm for computing the lattice of integral differential forms of a superelliptic curve over a local field. The only restriction is that the exponent of the superelliptic equation defining the curve is prime to the residue characteristic.
A key ingredient of the algorithm is the construction of a suitable model of the projective line whose normalisation in the function field of the curve has only rational singularities and can be used to compute the integral differentials. This construction is based on the theory of MacLane valuations. The talk is based on joint work with Stefan Wewers.