35
Views
2
CrossRef citations to date
0
Altmetric
Original Article

Painlevé VI Equations with Algebraic Solutions and Family of Curves

&
Pages 161-173 | Published online: 30 Jan 2011

  • Y. André. G-Functions and Geometry, Aspects of Mathematics E13. Braunschweig: Friedr. Vieweg & Sohn, 1989.
  • B. Ben Hamed and L. Gavrilov. "Families of Painlevé VI Equations Having a Common Solution." Int. Math. Res. Not. 60 (2005), 3727–52.
  • P. Boalch. "Painlevé Equations and Complex Reflections." Ann. Inst. Fourier 53:4 (2003), 1009–22.
  • P. Boalch. "Six Results on Painlevé VI, Théories Asymptotiques et Équations de Painlevé." In Sémin. Congr. 14, Soc. Math. France, edited by Éric Delabaere and Michéle Loday-Richaud, pp. 1–20. Paris: Université d'Angers, 2006.
  • S. Cantat and F. Loray. "Holomorphic Dynamics, Painlevé VI Equation and Character Varieties." arXiv :0711.1579v2, 1–69, 2007.
  • M. Dettweiler and S. Reiter. "An Algorithm of Katz and Its Application to the Inverse Galois Problem." J. Symbolic Comput. 30 (2000), 761–98.
  • M. Dettweiler and S. Reiter. "Middle Convolution of Fuchsian Systems and the Construction of Rigid Differential Systems." J. Algebra 318:1 (2007), 1–24.
  • M. Dettweiler and S. Reiter. "Painlevé Equations and the Middle Convolution." Adv. Geom. 7:3 (2007), 317–30.
  • C. F. Doran. "Algebraic and Geometric Isomonodromic Deformations." J. Differential Geom. 59:1 (2001), 33–85.
  • Y. Haraoka and G. Filipuk. "Middle Convolution and Deformation for Fuchsian Systems." J. Lond. Math. Soc. (2) 76:2 (2007), 438–50.
  • G.-M. Greuel, G. Pfister, and H. Schönemann. "Singular 2.0: A Computer Algebra System for Polynomial Computations." Centre for Computer Algebra, University of Kaiserslautern. Available online ( http://www.singular.uni-kl.de
  • P. A. Griffiths. "The Residue Calculus and Some Transcendental Results in Algebraic Geometry, I, II." Proc. Nat. Acad. Sci. USA. 55 (1966), 1303–09, 1392–95.
  • S. Herfurtner. "Elliptic Surfaces with Four Singular Fibres." Math. Ann. 291:2 (1991), 319–42.
  • K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida. From Gauss to Painlevé, Aspects of Mathematics E16. Braunschweig: Friedr. Vieweg & Sohn, 1991.
  • M. N. Katz. "Nilpotent Connections and the Monodromy Theorem: Applications of a Result of Turrittin." Inst. Hautes Études Sci. Publ. Math. 39 (1970), 175–232.
  • M. N. Katz. Rigid Local Systems, Annals of Mathematical Studies 139. Princeton: Princeton UP, 1996.
  • A. V. Kitaev. "Grothendieck's Dessins d'Enfants, Their Deformations, and Algebraic Solutions of the Sixth Painlevé and Gauss Hypergeometric Equations." Algebra i Analiz 17:1 (2005), 224–75.
  • F. Klein. 1884. Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, edited by Peter Slodowy. Basel: Birkhäuser and Stuttgart: B. G. Teubner, 1993.
  • H. Movasati. "On Ramanujan Relations between Eisenstein Series." In preparation, 2008.
  • H. Shiga, T. Tsutsui, and J. Wolfart. "Triangle Fuchsian Differential Equations with Apparent Singularities." Osaka J. Math. 41:3 (2004), 625–58.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.