Computing period matrices and the Abel-Jacobi map of superelliptic curves
Pascal Molin, Christian Neurohr · Mathematics of Computation · 2017
We present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation y m = f ( x ) y^m=f(x) . It relies on rigorous numerical integration of differentials between Weierstrass points, which is done using Gauss method if the curve is hyperelliptic ( m = 2 m=2 ) or the Double-Exponential method. The algorithm is implemented and makes it possible to reach thousands of digits accuracy even on large genus curves.