Duke Mathematical Journal

Moduli spaces of d-connections and difference Painlevé equations

Abstract

We show that difference Painlevé equations can be interpreted as isomorphisms of moduli spaces of difference connections (d-connections) on $\mathbb{P}^{\mathbf{1}}$ with given singularity structure. In particular, we derive a difference equation that lifts to an isomorphism between $A_2^{(1)*}$-surfaces in Sakai's classification (see [29]); it degenerates to both difference Painlevé V and classical (differential) Painlevé VI equations. This difference equation has been known before under the name of asymmetric discrete Painlevé IV equation

Article information

Source
Duke Math. J., Volume 134, Number 3 (2006), 515-556.

Dates
First available in Project Euclid: 28 August 2006

https://projecteuclid.org/euclid.dmj/1156771902

Digital Object Identifier
doi:10.1215/S0012-7094-06-13433-6

Mathematical Reviews number (MathSciNet)
MR2254625

Zentralblatt MATH identifier
1109.39019

Citation

Arinkin, D.; Borodin, A. Moduli spaces of d-connections and difference Painlevé equations. Duke Math. J. 134 (2006), no. 3, 515--556. doi:10.1215/S0012-7094-06-13433-6. https://projecteuclid.org/euclid.dmj/1156771902

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