2020/07/29 by Gendron, Quentin, Tahar, Guillaume · 2 citations
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2007.14872
The stratum H(a,-b1,…,-bp) of meromorphic 1-forms with a zero of order a and poles of orders b1,…,bp 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 (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.