PomeExample 21.13.35.74A6D2D50F46 Let us continue the example of $\mathbb {P}^2$ in example 21.13.12. We use the same notations. Take $\sigma _1$ as our reference cone, and $\rho _1=\sigma _5$, $\rho _2=\sigma _6$. Then
\[ Y_1=\Bigl \{ [X_0:0:X_2]:(X_0,X_2)\neq (0,0) \Bigr \} ,\quad Y_2=\Bigl \{ [X_0:0:0]:X_0\neq 0\Bigr \} . \]
The map $\Phi $ is given by
\[ \Phi (m_1,m_2)=(m_1,m_2). \]
In this case, we see easily
\[ \Delta _{Y_{\bullet }}\left(\mathcal{O}_{\mathbb {P}^2}(1)\right)=P_ D \]
is the polytope in 21.13.14.
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