2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98520We study complex projective surfaces admitting a Poisson structure. We prove a classification theorem and count how many independent Poisson structures there are on a given Poisson surface.LaTeX file, 8 pages; to be published in "Communications in Contemporary Mathematics"Algebraic Geometry14J26,53D17text