论文标题
同意振动和共振安排
Isoresidual fibration and resonance arrangements
论文作者
论文摘要
Meromorphic $ 1 $ 1 $ -Forms的层$ \ MATHCAL {h}（a，-b_ {1}，\ dots，-b_ {p}）$，带有订单$ a $ a $ a $ a $ a $ a $ a $ a $ a和por的订单$ b_ {1}的订单$ b_ {1}，\ dots，b_ {p} $ by b_ {p} $ aprye a Is a Is a Is a iS a Is a iS a iS a Is a iS a iS a iS a iS a iS a Is a Ise的订单，在两极的残留物差异。我们表明，在超平面布置的补充，共振布置的补充上，同层纤维是$ \ frac {a！} {（a+2-p）！} $的封面。此外，计算具有最多三极的地层的纤维化单构型，并为所有地层提供了发电机和关系系统。这些结果是通过将树的特殊差异关联而获得的，并研究了这些树的几何特性与这些树的组合特性之间的关系。
The stratum $\mathcal{H}(a,-b_{1},\dots,-b_{p})$ of meromorphic $1$-forms with a zero of order $a$ and poles of orders $b_{1},\dots,b_{p}$ on the Riemann sphere has a map, the isoresidual fibration, defined by assigning to any differential its residues at the poles. We show that above the complement of a hyperplane arrangement, the resonance arrangement, the isoresidual fibration is an unramified cover of degree $\frac{a!}{(a+2-p)!}$. Moreover, the monodromy of the fibration is computed for strata with at most three poles and a system of generators and relations is given for all strata. These results are obtained by associating to special differentials of the strata a tree, and by studying the relationship between the geometric properties of the differentials and the combinatorial properties of these trees.
