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SIGMA, 2018, Volume 14, 111, 22 pages (Mi sigma1410)  

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.

Funding Agency Grant Number
Japan Society for the Promotion of Science 18J00245
The author is supported by Grant-in-Aid for JSPS Research Fellows Number 18J00245.


DOI: https://doi.org/10.3842/SIGMA.2018.111

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Full text: https://www.imath.kiev.ua/~sigma/2018/111/
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ArXiv: 1710.03977
MSC: 14D20; 34M56
Received: January 23, 2018; in final form October 3, 2018; Published online October 13, 2018
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Citation: Arata Komyo, “The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations”, SIGMA, 14 (2018), 111, 22 pp.

Citation in format AMSBIB
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\paper The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations
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\vol 14
\papernumber 111
\totalpages 22
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