In algebraic geometry , Chow's moving lemma , proved by Wei-Liang ( 1956 ) , states: given algebraic cycles Y , Z on a nonsingular quasi-projective variety X , there is another algebraic cycle Z' which is rationally equivalent to Z on X, such that Y and Z' intersect properly. The lemma is one of the key ingredients in developing intersection theory and the Chow ring , 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 Z' to be effective.
References Chow, Wei-Liang (1956), "On equivalence classes of cycles in an algebraic variety", Annals of Mathematics 64 (3): 450– 479, doi :10.2307/1969596, ISSN 0003-486X, JSTOR 1969596, MR 0082173Hartshorne, Robin (1977), Algebraic Geometry Graduate Texts in Mathematics , vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9 , MR 0463157Roberts, Joel (1972). "Chow's moving lemma. Appendix 2 to: "Motives" by Steven L. Kleiman.". Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer School in Math.) . Groningen, Wolters-Noordhoff. pp. 89– 96. ISBN 9001670806 . MR 0382269. OCLC 579160. 