2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70062We introduce deformation theoretic methods for determining when a curve $X$ in a non-hyperelliptic jacobian $JC$ will deform with $JC$ to a non-jacobian. We apply these methods to a particular class of curves in symmetric powers $C^{(e)}$ of $C$ where $3\leq e\leq g-3$. More precisely, given a pencil $g^1_d$ of degree $d$ on $C$, let $X$ be the curve parametrizing divisors of degree $e$ in divisors of $g^1_d$ (see the paper for the precise scheme-theoretical definition). Under certain genericity assumptions on the pair $(C, g^1_d)$, we prove that if $X$ deforms infinitesimally out of the jacobian locus with $JC$ then either $d=2e$, dim$H^0 (g^1_d) = e$ or $d=2e+1$, dim$H^0 (g^1_d) = e+1$. The analogous result in the case $e=2$ without genericity assumptions was proved earlier.ams-latex, 27 pagesAlgebraic GeometryPrimary 14K12, 14C25; Secondary 14B10, 14H40text