Explicit algebraic description of hyperelliptic Jacobians on the basis of the Klein \(\sigma\)-functions
Let \(V\) be an affine hyperelliptic curve of genus \(g\). Using the classical theory of Klein's \(\sigma\)-function explicit algebraic equations for (an affine part of) the Jacobian of \(V\) are developed. This is a generalization of the classical equation of a plane elliptic curve in terms of the Weierstrass \(\wp\)-function. The paper presents no proofs at all.
scientific article; zbMATH DE number 1002981