The Stacks project

Example 31.23.2. Let $A = \mathbf{C}[x, \{ y_\alpha \} _{\alpha \in \mathbf{C}}]/ ((x - \alpha )y_\alpha , y_\alpha y_\beta )$. Any element of $A$ can be written uniquely as $f(x) + \sum \lambda _\alpha y_\alpha $ with $f(x) \in \mathbf{C}[x]$ and $\lambda _\alpha \in \mathbf{C}$. Let $X = \mathop{\mathrm{Spec}}(A)$. In this case $\mathcal{O}_ X = \mathcal{K}_ X$, since on any affine open $D(f)$ the ring $A_ f$ any nonzerodivisor is a unit (proof omitted).

Comments (0)

There are also:

  • 6 comment(s) on Section 31.23: Meromorphic functions and sections

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Your email address will not be published.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 01X3. Beware of the difference between the letter 'O' and the digit '0'.



View Example 31.23.2 as pdf