In algebraic geometry, Chow's moving lemma, proved by , states: given

algebraic cycles In mathematics, an algebraic cycle on an algebraic variety ''V'' is a formal linear combination of subvarieties of ''V''. These are the part of the algebraic topology of ''V'' that is directly accessible by algebraic methods. Understanding the alg ...

''Y'', ''Z'' on a

nonsingular In linear algebra, an -by- square matrix is called invertible (also nonsingular or nondegenerate), if there exists an -by- square matrix such that :\mathbf = \mathbf = \mathbf_n \ where denotes the -by- identity matrix and the multiplica ...

quasi-projective variety In mathematics, a quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space of a Zariski-open and a Zariski-closed subset. A similar definition is used in ...

''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 In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem o ...

, 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.

References

* * Theorems in algebraic geometry Zhou, Weiliang {{algebraic-geometry-stub