Moduli spaces of d-connections and difference Painlevé equations
Arinkin, D. ; Borodin, A.
Duke Math. J., Tome 131 (2006) no. 1, p. 515-556 / Harvested from Project Euclid
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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
Publié le : 2006-09-15
Classification:  39A10,  14H60 
@article{1156771902,
     author = {Arinkin, D. and Borodin, A.},
     title = {Moduli spaces of d-connections and difference Painlev\'e equations},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 515-556},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1156771902}
}

Arinkin, D.; Borodin, A. Moduli spaces of d-connections and difference Painlevé equations. Duke Math. J., Tome 131 (2006) no. 1, pp.  515-556. http://gdmltest.u-ga.fr/item/1156771902/