Jacobian variety of generalized Fermat curves (Q2814322)

Let us have two integers \(p, n \geq 2\). A closed Riemann surface \(S\) is a generalized Fermat curve of type \((p, n)\) if it admits a group of conformal automorphisms \(H\approx (\mathbb{Z}/p\mathbb{Z})^n\), such that the orbifold \(S/H\) is the Riemann sphere with \(n+1\) branch points of order \(p\). In the paper under review, the authors obtain an isogenous decomposition of the Jacobian variety \(JS\) of generalized Fermat curves \(S\) of type \((p, n)\), as a product of the Jacobian varieties of certain cyclic \(p\)-gonal curves. Besides, they give explicit equations of these curves in terms of the equations of \(S\).