algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, Chow's moving lemma, proved by , states: given algebraic cycles ''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 multiplicati ...

quasi-projective variety ''X'', there is another algebraic cycle ''Z' '' on ''X'' such that ''Z' '' is

rationally equivalent In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined inte ...

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.

References

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