What is the "theorem of the cube" for abelian varieties? What is the statement and how should I think about it?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
If you have a line bundle trivial on 3 "surfaces" of a "cube" See wikipedia. 


One application of the theorem of the cube is to study the map from an abelian variety A to its dual abelian variety; the map is defined in terms of line bundles and the key technical theorem one uses to prove anything (e.g. that the map to the dual is a homomorphism) is the theorem of the cube. See Mumford's Abelian Varieties book or Martin Olsson's notes from this summer's Hangzhou workshop. 

