Journal of the Mathematical Society of Japan

Moduli of regular singular parabolic connections with given spectral type on smooth projective curves

Michi-aki INABA and Masa-Hiko SAITO

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We define a moduli space of stable regular singular parabolic connections with given spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we define the isomonodromic deformation on this moduli space and prove the geometric Painlevé property of the isomonodromic deformation.


This work was partly supported by JSPS KAKENHI: Grant Numbers JP17H06127, JP15K13427, JP24224001, JP22740014, JP26400043.

Article information

J. Math. Soc. Japan, Volume 70, Number 3 (2018), 879-894.

Received: 6 November 2016
First available in Project Euclid: 31 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 34M56: Isomonodromic deformations 34M55: Painlevé and other special equations; classification, hierarchies;

regular singular connection of spectral type moduli space of parabolic connections symplectic structure Riemann–Hilbert correspondence geometric Painlevé property isomonodromic deformation of linear connection higher dimensional Painlevé equations


INABA, Michi-aki; SAITO, Masa-Hiko. Moduli of regular singular parabolic connections with given spectral type on smooth projective curves. J. Math. Soc. Japan 70 (2018), no. 3, 879--894. doi:10.2969/jmsj/76597659.

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