15 September 2006 Moduli spaces of d-connections and difference Painlevé equations
D. Arinkin, A. Borodin
Author Affiliations +
Duke Math. J. 134(3): 515-556 (15 September 2006). DOI: 10.1215/S0012-7094-06-13433-6

Abstract

We show that difference Painlevé equations can be interpreted as isomorphisms of moduli spaces of difference connections (d-connections) on P1 with given singularity structure. In particular, we derive a difference equation that lifts to an isomorphism between A2(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

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D. Arinkin. A. Borodin. "Moduli spaces of d-connections and difference Painlevé equations." Duke Math. J. 134 (3) 515 - 556, 15 September 2006. https://doi.org/10.1215/S0012-7094-06-13433-6

Information

Published: 15 September 2006
First available in Project Euclid: 28 August 2006

zbMATH: 1109.39019
MathSciNet: MR2254625
Digital Object Identifier: 10.1215/S0012-7094-06-13433-6

Subjects:
Primary: 39A10
Secondary: 14H60

Rights: Copyright © 2006 Duke University Press

Vol.134 • No. 3 • 15 September 2006
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