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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Abstract

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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1527795357

Digital Object Identifier
doi:10.2969/jmsj/76597659

Mathematical Reviews number (MathSciNet)
MR3832081

Zentralblatt MATH identifier
06966965

Subjects
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;

Keywords
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

Citation

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. https://projecteuclid.org/euclid.jmsj/1527795357


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References

  • W. Crawley-Boevey, Indecomposable parabolic bundles and the existence of matrices in prescribed conjugacy class closures with product equal to the identity, Publ. Math. Inst. Hautes Études Sci., 100 (2004), 171–207.
  • K. Fuji and T. Suzuki, Drinfeld–Sokolov hierarchies of type A and fourth order Painlevé system, Funkcial. Ekvac., 53 (2010), 143–167.
  • K. Fuji and T. Suzuki, Higher order Painlevé system of type $D^{(1)}_{2n+2}$ arising from integrable hierarchy, Int. Math. Res. Not. IMRN, 2008 (2008), Art.ID rnm129.
  • M. Inaba, Moduli of parabolic connections on a curve and Riemann–Hilbert correspondence, J. Algebraic Geom., 22 (2013), 407–480.
  • M. Inaba, K. Iwasaki and M.-H. Saito, Moduli of stable parabolic connections, Riemann–Hilbert correspondence and geometry of painlevé equation of type VI, Part I, Publ. Res. Inst. Math. Sci., 42 (2006), 987–1089.
  • M. Inaba, K. Iwasaki and M.-H. Saito, Dynamics of the sixth Pailevé Equations, in Théories asymptotiques et équations de Painlevé, Sémin. Congr., 14, Soc. Math. France, Paris, 2006, 103–167.
  • H. Kawakami, A. Nakamura and H. Sakai, Degeneration scheme of 4-dimensional Painlevé equations, arXiv:1209.3836.
  • H. Kawakami, A. Nakamura and H. Sakai, Toward a classification of four-dimensional Painlevé-type equations, Algebraic and geometric aspects of integrable systems and random matrices, Contemp. Math., 593, Amer. Math. Soc., Providence, RI, 2013, 143–161.
  • T. Oshima, Classification of Fuchsian systems and their connection problem, Exact WKB analysis and microlocal analysis, RIMS Kôkyûroku Bessatsu, B37, Res. Inst. Math. Sci. (RIMS), Kyoto, 2013, arXiv:0811.2916v2, 163–192.
  • M.-H. Saito and S. Szabo, Apparent singularities and canonical coordinates for moduli of parabolic connections and parabolic Higgs bundles, in preparation.
  • H. Sakai, Isomonodromic deformation and $4$-dimensional Painlevé type equations, preprint, University of Tokyo, Mathematical Sciences, 2010.
  • Y. Sasano, Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type $D^{(1)}_6$, II, RIMS Kôkyûroku Bessatsu B5, 2008, 137–152.
  • D. Yamakawa, Geometry of multiplicative preprojective algebra, Int. Math. Res. Pap. IMRP 2008, Art. ID rpn008, 77pp. (arXiv:0710.10.2649v4 [math.SG] 15 Nov 2007)