2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114090We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C})\otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})$, where $X$ is a compact Kähler variety without Albanese fibrations.11 pages, to appear in Manuscripta MathematicaAlgebraic Geometry32J27; 32J25text