Definition 9.10.6C9A9F3CE78E7

Definition 9.10.6.C9A9F3CE78E7 A modification of a compact complex space $X$ is a finite composition of blow-ups with smooth centers.

We say a modification $\pi '\colon Z\rightarrow X$ dominates another $\pi \colon Y\rightarrow X$ if there is a morphism $g\colon Z\rightarrow Y$ of complex spaces making the following diagram commutative:

8D4BB1A6524D 9.10.7