The Stacks project

Definition 29.57.1. Let $f : X \to Y$ be a morphism of schemes.

  1. We say the integer $n$ bounds the degrees of the fibres of $f$ if for all $y \in Y$ the fibre $X_ y$ is a finite scheme over $\kappa (y)$ whose degree over $\kappa (y)$ is $\leq n$.

  2. We say the fibres of $f$ are universally bounded1 if there exists an integer $n$ which bounds the degrees of the fibres of $f$.

[1] This is probably nonstandard notation.

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Your email address will not be published.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 03J4. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 29.57.1 as pdf