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

Monodromy problem and Tangential center-focus problem for product of generic lines in $\mathbb{P}^2$