Isoresidual fibration and resonance arrangements

The stratum $$\mathcal {H}(a,-b_{1},\dots ,-b_{p})$$ of meromorphic 1-forms with a zero order and poles orders $$b_{1},\dots ,b_{p}$$ on the Riemann sphere has map, isoresidual fibration, defined by assigning to any differential its residues at poles. We show that above complement hyperplane arrangement, resonance fibration is an unramified cover degree $$\frac{a!}{(a+2-p)!}$$ . Moreover, monodromy computed for strata most three system generators relations given all strata. These results are obtained associating special differentials tree studying relationship between geometric properties combinatorial these trees.