If "Z" is a prime Weil divisor on "X", then formula_74 is a closed irreducible subscheme of "Y". Depending on φ, it may or may not be a prime Weil divisor. For example, if φ is the blow up of a point in the plane and "Z" is the exceptional divisor, then its image is not a Weil divisor. Therefore φ*"Z" is defined to be formula_74 if that subscheme is a prime divisor and is defined to be the zero divisor otherwise. Extending this by linearity will, assuming "X" is quasi-compact, define a homomorphism called the pushforward. (If "X" is not quasi-compact, then the pushforward may fail to be a locally finite sum.) This is a special case of the pushforward on Chow groups.