2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166791Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic curves on any surface of general type with two linearly independent regular one forms.13 pagesAlgebraic GeometryComplex Variables14C17, 14E30, 14G25, 14H45, 14J29, 14K12, 32Q45, 32Q57text