Lemma 1.20 . [04RY]

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Lemma 1.20.

Let $\Delta^{\prime}\subset\Delta$ be a face. The intersection $V\cap\mathbb{C}T_{\Delta^{\prime}}$ coincides with the hypersurface cut on $\mathbb{C}T_{\Delta^{\prime}}$ by the closure of the zero set of the following $\Delta^{\prime}$ -truncation of the polynomial $f$

f_{\Delta^{\prime}}(z)=\sum\limits_{j\in\Delta^{\prime}}a_{j}z^{j}.