Isoperiodic meromorphic forms: two simple poles

2021/09/04 by Calsamiglia, Gabriel, Deroin, Bertrand
#14H15 #30F30 #32G13 #53A30 #57M50 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.01796

Abstract

In this paper we prove that isoperiodic moduli spaces of meromorphic differentials with two simple poles on homologically marked smooth curves are non empty and connected, unless they correspond to double covers of ℂ/ℤ on curves of genus at least two. We deduce dynamical consequences for the corresponding isoperiodic foliation.

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