2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201537We show that complex multiplication on abelian varieties is equivalent to the existence of a constant rational Kähler metric. We give a sufficient condition for a mirror of an abelian variety of CM-type to be of CM-type as well. We also study the relationship between complex multiplication and rationality of a toroidal lattice vertex algebra.22 pages, introduction and exposition of results rewritten, references addedAlgebraic GeometryHigh Energy Physics - TheoryMathematical Physicstext