Chow's moving lemma
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In algebraic geometry, Chow's moving lemma, proved by Wei-Liang Chow (1956), states: given algebraic cycles Y, Z on a nonsingular quasi-projective variety X, there is another algebraic cycle Z' on X such that Z' is rationally equivalent to Z and Y and Z' intersect properly. The lemma is one of key ingredients in developing the intersection theory, as it is used to show the uniqueness of the theory.
Even if Z is an effective cycle, it is not in general possible to choose the cycle Z' to be effective.
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