Exercise 111.54.4. Let $k$ be a field. Let $X$ be a “triangle” over $k$, i.e., you get $X$ by glueing three copies of $\mathbf{A}^1_ k$ to each other by identifying $0$ on the first copy to $1$ on the second copy, $0$ on the second copy to $1$ on the third copy, and $0$ on the third copy to $1$ on the first copy. It turns out that $X$ is isomorphic to $\mathop{\mathrm{Spec}}(k[x, y]/(xy(x + y + 1)))$; feel free to use this. Compute the Picard group of $X$.

## 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Your email address will not be published.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)