### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 111, 22 pages      arXiv:1710.03977      https://doi.org/10.3842/SIGMA.2018.111

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

Arata Komyo
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received January 23, 2018, in final form October 03, 2018; Published online October 13, 2018

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.

Key words: parabolic connection; quadratic differential; isomonodromic deformation; twisted cotangent bundle.

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