Theorem of the cube
algebraic geometry theorem that, for any complete varieties U, V and W over an algebraically closed field, given points u, v and w on them, any invertible sheaf which has a trivial restriction to each of U×V×{w}, U×{v}×W and {u}×V×W is itself trivial
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 (1959), who credited it to...
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