2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161461We study the second Gaussian map for a curve X of genus g, in relation with the second fundamental form of the period map. We exhibit a class of infinitely many curves with surjective second Gaussian map. We compute its rank on the hyperelliptic and trigonal locus and show global generation of its image for X not hyperelliptic nor trigonal.Algebraic Geometry14H10; 14h40; 14H45; 14H51text