and $f(x_1, \ldots, x_n)x_{n+1} - 1$. Thus, $k[U] = k[X]_{\bar f}$, where $\bar f$ is the image of $f$ in $k[X]$ and the subscript indicates localization . The inclusion morphism $U \to X$ corresponds to the standard homomorphism $k[X] \to k[X]_{\bar f}$. It would be good to work this out! share