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The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations (1710.03977v4)
Published 11 Oct 2017 in math.AG
Abstract: In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which are phase spaces of isomonodromic deformation systems). Moreover, we see that the moduli spaces of parabolic connections with a quadratic differential are equipped with structures of twisted cotangent bundles.