The Stacks project

Definition 41.21.1. Let $X$ be a locally Noetherian scheme. A strict normal crossings divisor on $X$ is an effective Cartier divisor $D \subset X$ such that for every $p \in D$ the local ring $\mathcal{O}_{X, p}$ is regular and there exists a regular system of parameters $x_1, \ldots , x_ d \in \mathfrak m_ p$ and $1 \leq r \leq d$ such that $D$ is cut out by $x_1 \ldots x_ r$ in $\mathcal{O}_{X, p}$.