Exercise 110.37.9. Let $S$ be a graded ring. Let $X = \text{Proj}(S)$. Let $Z, Z' \subset X$ be two closed subschemes. Let $\varphi : Z \to Z'$ be an isomorphism. Assume $Z \cap Z' = \emptyset $. Show that for any $z \in Z$ there exists an affine open $U \subset X$ such that $z \in U$, $\varphi (z) \in U$ and $\varphi (Z \cap U) = Z' \cap U$. (Hint: Use Exercise 110.37.8 and something akin to Schemes, Lemma 26.11.5.)

## 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Your email address will not be published.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)