Symmetric correspondences with decomposable minimal equation

Abstract

We study symmetric correspondences with completely decomposable minimal equation on smooth projective curves $C$. The Jacobian of $C$ then decomposes correspondingly. For all positive integers $g$ and $\ell$, we give series of examples of smooth curves $C$ of genus $n^{\ell }(g-1)+1$ with correspondences satisfying minimal equations of degree $\ell +1$ such that the Jacobian of $C$ has at least $2^{\ell }$ isogeny components.