The Stacks project

Lemma 43.13.1. Let $X$ and $Y$ be varieties. Then $X \times Y$ is a variety and $\dim (X \times Y) = \dim (X) + \dim (Y)$.

Proof. The scheme $X \times Y = X \times _{\mathop{\mathrm{Spec}}(\mathbf{C})} Y$ is a variety by Varieties, Lemma 33.3.3. The statement on dimension is Varieties, Lemma 33.20.5. $\square$


Comments (0)

There are also:

  • 3 comment(s) on Section 43.13: Proper intersections

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Your email address will not be published.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