2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97954We prove that for every compact Kähler manifold $X$ there exists an $L$-infinity morphism, lifting the usual cup product in cohomology, from the Kodaira-Spencer differential graded Lie algebra to the suspension of the space of linear endomorphisms of the singular cohomology of $X$. As a consequence we get an algebraic proof of the principle ``obstructions to deformations of compact Kaehler manifolds annihilate ambient cohomology''.Latex-10 pagesAlgebraic Geometry32G05text