Let $\mathcal{F}=(X,\omega,f,B)$ be any generic-singular fibration and $F_{\bar{b}}=f^{-1}(\bar{b})$ a smooth fibre. There is a basis of $H_{1}(F_{\bar{b}},\mathbb{Z})$ whose corresponding basis $\lambda_{1},\lambda_{2},\lambda_{3}$ of the period lattice $\Lambda$ of $\mathcal{F}$, in the coordinates $b=(b_{1},b_{2},b_{3})$ on $B\cong D^{2}\times D^{1}$ given by Theorem 4.6, can be written as

$$\lambda_{1}=\lambda_{0}+dH,\qquad\lambda_{2}=2\pi db_{2},\qquad\lambda_{3}=db_{3},$$

(17)

where $H\in C^{\infty}(B)$ is such that $H(0)=0$ and $\lambda_{0}=-\log|b_{1}+ib_{2}|db_{1}+\Arg(b_{1}+ib_{2})db_{2}$. The monodromy of $\Lambda$ is given by

$$\left(\begin{array}[]{ccc}1&0&0\\ 1&1&0\\ 0&0&1\end{array}\right).$$

(18)