Divisibility of ideals and blowing up

摘要

Let R be a Noetherian integral domain, let V=Spec (r), and let I, J be nonzero ideals of R. Clearly, if J is either a divisor of I or a power of I there is a map BlI (V) →BlJ(V) of schemes voer V. The purpose of this note is to prove, conversely, that if such a map Exists, then J must be a fractional ideal divisor of some power of I.