2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103852We study the $A$-discriminant of toric varieties. We reduce its computation to the case of irreducible configurations and describe its behavior under specialization of some of the variables to zero. We prove a Gale dual characterization of dual defect toric varieties and deduce from it the classsification of such varieties in codimension less than or equal to four. This classification motivates a decomposition theorem which yields a sufficient condition for a toric variety to be dual defect. For codimension less than or equal to four, this condition is also necessary and we expect this to be the case in general.22 pages; In addition to minor corrections, Section 5 has been expanded and rewritten to include a Gale dual characterization of dual defect toric varietiesAlgebraic Geometry14M25; 13P05text