2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155467Let $X$ be a connected compact complex manifold admitting a finite surjective map $A \to X$ from a complex torus $A.$ We prove that up to finite étale cover, $X$ is a product of projective spaces and a torus.final version, to appear in Journal of Geometric AnalysisAlgebraic Geometry32J27, 14M17, 14J40text