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

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.

References in corpus (3)

• On the Geometry of Isomonodromic Deformations
• Theta Functions and Szegö Kernels
• Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections