Pullback of a Cartier divisor ($f^{\ast }D$)

For a morphism of varieties $f:X\to Y$, pull back local defining rational functions of a Cartier divisor $D$ whenever they remain nonzero on each component of $X$. Their ratios remain regular units, defining $f^{\ast }D$. Equivalently, pull back the associated line bundle and its rational section. A dominant morphism always permits this construction.