2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147219Van Geemen and van der Geer, Donagi, Beauville and Debarre proposed characterizations of the locus of jacobians which use the linear system of $2Θ$-divisors. We give new evidence for these conjectures in the case of Prym varieties.AMS-Latex, 11 pages, the exposition has been modified, Proposition 5 has been modifiedAlgebraic Geometry14H42 (Primary) 14K25 (Secondary)text