Theorem of the cube 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 , who credited it to André Weil. A discussion of the history has been given by . A treatment by means of sheaf cohomology, and description in terms of the Picard functor, was given by . The theorem states that for
Nth root real number is a positive real number, negative numbers do not have real square roots. However, for every negative real number there are two imaginary square roots. For example, the square roots of −25 are 5"i" and −5"i", where "i" represents a number whose square is . A cube root of a number "x" is a number "r" whose cube is "x": Every real number "x" has exactly one real cube root, written formula_4. For example, Every real number has two additional complex cube roots. Expressing the degree of an "n"th root in its exponent form, as in formula_37, makes