Let $X$ be smooth surface, such that $f:X\dashrightarrow \Bbb{A}^1\subset \Bbb{P}^1$ is a rational map, we have the standard result that the rational map into projective space has undetermined locus of codimension $\ge 2$.
However by definition over the undetermined point $p\in X$ there exist a $f_1,f_2 \in \mathcal{O}_{X,p}$ such that $f_2(p) = 0$ and $f_1/f_2 = f$ locally, since the vanishing locus of $f_2$ say $V(f_2)$ has codimension 1, does this means that undetermined locus is codimension 1.
I know there must be something wrong since the undetermined locus is codimension $\ge 2$, not 1.