The monodromy along the loop $\gamma$, of the $\mathbb{Z}$-affine structure induced by $\rho$ on $U_{i_{m}}\cup U_{i_{m^{\prime}}}$ is

(3.2.3)

$$T_{\rho}(\gamma)=\left(\begin{matrix}1&0&0&\ldots&0\\ b_{i_{1}}-b^{\prime}_{i_{1}}&1&0&\ldots&0\\ b_{i_{2}}-b^{\prime}_{i_{2}}&0&1&\ldots&0\\ \vdots&\vdots&&\ddots&\\ b_{i_{n-1}}-b^{\prime}_{i_{n-1}}&0&0&\ldots&1\end{matrix}\right)$$

with respect to the basis $(v_{D_{i_{0}}},v_{D_{i_{1}}},\ldots,v_{D_{i_{n-1}}})$ and origin $v_{D_{i_{n}}}$.