Pullback of a Cartier divisor
= Pullback of a Cartier divisor
{title2=$f^*D$}
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 $f^*D$. Equivalently, pull back the associated <line bundle> and its rational section. A dominant morphism always permits this construction.