论文标题
$ \ mathbb {p}^2 $中通用线的产物产物的单片问题和切向中心对焦问题
Monodromy problem and Tangential center-focus problem for product of generic lines in $\mathbb{P}^2$
论文作者
论文摘要
我们考虑了由一般位置的产品产品商的商人定义的理性地图$ f $，我们研究了与$ f $相关的纤维化的单片问题和切向中心对焦问题。因此，我们研究了单型动作轨道在消失的周期中产生的1个常规纤维的1个理学组的子模块。此外，我们表征了$ \ mathbb {p}^2 $中的meromorphic 1-forms $ω$，以使Abelian积分$ \ int_ {δ_t}ω$ $在一个循环$Δ_T$上消失了中心周围的循环$Δ_T$。
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 $ω$ in $\mathbb{P}^2$ such that the Abelian integral $\int_{δ_t}ω$ vanishes on a family of cycles $δ_t$ around a center singularity.
