What is Theorem of the cube?

In mathematics, the theorem of the cube is a condition for a line bundle over a product of three complete varieties to be trivial. It was a principle discovered, in the context of linear equivalence, by the Italian school of algebraic geometry. The final version of the theorem of the cube was first published by Lang , who credited it to André Weil. A discussion of the history has been given by Kleiman. A treatment by means of sheaf cohomology, and description in terms of the Picard functor, was given by Mumford.