Formulas for Differentiating Hyperelliptic Functions with Respect to Parameters and Periods
摘要
Abstract
By explicitly solving the problem of differentiating hyperelliptic functions with respect to parameters, we derive explicit formulas for the Christoffel symbols of the Gauss–Manin connection in the universal bundle of hyperelliptic curves; as a consequence, we obtain a solution to the problem of differentiating hyperelliptic functions with respect to periods.