Duke Mathematical Journal
- Duke Math. J.
- Volume 134, Number 3 (2006), 515-556.
Moduli spaces of d-connections and difference Painlevé equations
We show that difference Painlevé equations can be interpreted as isomorphisms of moduli spaces of difference connections (d-connections) on with given singularity structure. In particular, we derive a difference equation that lifts to an isomorphism between -surfaces in Sakai's classification (see ); 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
Duke Math. J., Volume 134, Number 3 (2006), 515-556.
First available in Project Euclid: 28 August 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 39A10: Difference equations, additive
Secondary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]
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