  We consider the rational map $F$ defined by the quotient of products of lines
in general position and we study the monodromy problem and tangential
center-focus problem for the fibration associated with $F$. Thus, we study the
submodule of the 1-homology group of a regular fiber of $F$ generated by the
orbit of the monodromy action on a vanishing cycle. Moreover, we characterize
the meromorphic 1-forms $\omega$ in $\mathbb{P}^2$ such that the Abelian
integral $\int_{\delta_t}\omega$ vanishes on a family of cycles $\delta_t$
around a center singularity.
