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In this paper, we study the moduli spaces of parabolic connections with aquadratic differential. We endow these moduli spaces with symplectic structuresby using the fundamental 2-forms on the moduli spaces of parabolic connections(which are phase spaces of isomonodromic deformation systems). Moreover, we seethat the moduli spaces of parabolic connections with a quadratic differentialare equipped with structures of twisted cotangent bundles.

The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations