What is the "theorem of the cube" for abelian varieties? What is the statement and how should I think about it?



What is the Theorem of the Cube?
If you have a line bundle trivial on 3 "surfaces" of a "cube" $A\times B\times C$ where $A$, $B$, $C$ are abelian varieties, then this line bundle in trivial on the whole "cube".


See [wikipedia](http://en.wikipedia.org/wiki/Theorem%20of%20the%20cube).


