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

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.

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

MSC: 14D20; 34M56

Received: January 23, 2018; in final form October 3, 2018; Published online October 13, 2018

Language: English

DOI: 10.3842/SIGMA.2018.111

Bibliographic databases:

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ArXiv: 1710.03977