2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101114A new tautological equation of $\Mbar_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.Algebraic GeometryTautological equation in \bar{M}_{3,1} via invariance conjecturestext