- Show that \({\mathbf{P}}^n\times {\mathbf{P}}^m\) is rational
\(\left[x_0: x_1: \ldots: x_n\right] \times\left[y_0: y_1: \ldots: y_m\right] \rightarrow\left[1: \frac{x_1}{x_0}: \frac{x_2}{x_0}: \ldots: \frac{x_n}{x_0}: \frac{y_1}{y_0}: \frac{y_2}{y_0}, \ldots: \frac{y_n}{y_0}\right]\) This has inverse \(\left[1: z_1: \ldots: z_{n+m}\right] \rightarrow\left[1: z_1: \ldots: z_n\right] \times\left[1: z_{n+1}: \ldots: z_{n+m}\right]\)