2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115348Let X_g=C^{(2)}_g be the second symmetric product of a very general curve of genus g. We reduce the problem of describing the ample cone on X_g to a problem involving the Seshadri constant of a point on X_{g-1}. Using this we recover a result of Ciliberto-Kouvidakis that reduces finding the ample cone of X_g to the Nagata conjecture when g\ge 9. We also give new bounds on the the ample cone of X_g when g=5.Minor corrections, mostly typographical and exposition improvedAlgebraic Geometry14C20, 14Q10text