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 $\mathcal{O}_{X, p}$.

## Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)