Moduli spaces of \(d\)-connections and difference Painlevé equations. (English) Zbl 1109.39019

Authors’ abstract: We show that difference Painlevé equations can be interpreted as ismorphisms of moduli spaces of difference connections on \(\mathbb P^1\) with given singularity structure. In particular, we derive a difference equation that lifts to an isomorphism between \(A_2^{(1)*}\)-surfaces is in H. Sakai’s classification [Commun. Math. Phys. 220, No. 1, 165–229 (2001; Zbl 1010.34083)]; 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.
Reviewer: Eduardo Liz (Vigo)


39A12 Discrete version of topics in analysis
39A10 Additive difference equations
14H60 Vector bundles on curves and their moduli
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies


Zbl 1010.34083
Full Text: DOI arXiv Euclid


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