What is the "theorem of the cube" for abelian varieties? What is the statement and how should I think about it?
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If you have a line bundle trivial on 3 "surfaces" of a "cube" See wikipedia. |
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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. |
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