The Stacks project

Definition 115.23.9. Let $X$ be a scheme. Let $\{ D_ i\} _{i \in I}$ be a locally finite collection of effective Cartier divisors on $X$. Suppose given a function $I \to \mathbf{Z}_{\geq 0}$, $i \mapsto n_ i$. The sum of the effective Cartier divisors $D = \sum n_ i D_ i$, is the unique effective Cartier divisor $D \subset X$ such that on any quasi-compact open $U \subset X$ we have $D|_ U = \sum _{D_ i \cap U \not= \emptyset } n_ iD_ i|_ U$ is the sum as in Divisors, Definition 31.13.6.

Comments (0)

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Your email address will not be published.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.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 02T3. Beware of the difference between the letter 'O' and the digit '0'.