Let $X_{\Sigma} = \mathbb{P}_{X_{\Sigma'}}(\mathcal{L_1}\oplus\mathcal{L_2}),X_{\Sigma'}$ be toric varieties ('good' if it's necessary), $\mathcal{L}_i\in \mathrm{Pic}(X_{\Sigma'})$ and $\pi:X_{\Sigma}\to X_{\Sigma'}$ be a morphism of projection. For example $X_{\Sigma'} = \mathbb{P}^1$ and $X_{\Sigma} = \mathbb{P}_{\mathbb{P}^1}(\mathcal{O} \oplus \mathcal{O}(d))$
So my question is how to express twisting sheaf $\mathcal{O}_{X_{\Sigma}}(1)$ in terms of $\Sigma$ or $\Sigma'$.
More precisely there is a representation of $\mathcal{O}_{X_{\Sigma}}(1) = \sum a_i D_i$ as sum of $T$-stable divisors which are correspond to rays of $\Sigma$ and i want determine $a_i$.