The trigonal construction in the ramified case

Abstract To every double cover ramified in two points of a general trigonal curve of genus g$g$, one can associate an étale double cover of a tetragonal curve of genus g+1$g+1$. We show that the corresponding Prym varieties are canonically isomorphic as principally polarized abelian varieties. This extends Recillas' trigonal construction to covers ramified in two points.To every double cover ramified in two points of a general trigonal curve of genus g, one can associate an étale double cover of a tetragonal curve of genus g + 1. We show that the corresponding Prym varieties are canonically isomorphic as principally polarized abelian varieties. This extends Recillas' trigonal construction to covers ramified in two points.Peer Reviewe