Restriction of A-Discriminants and Dual Defect Toric Varieties
  We 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. 
Raymond Curran and Eduardo Cattani