2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112746We prove that, for every compact Kaehler manifold, the period map of its Kuranishi family is induced by a natural L-infinity morphism. This implies, by standard facts about L-infinity algebras, that the period map is a "morphism of deformation theories" and then commutes with all deformation theoretic constructions (e.g. obstructions).31 pages, uses xypicAlgebraic GeometryQuantum Algebra14D07, 17B70, 13D10text