Quantization of hyper-elliptic curves from isomonodromic systems and topological recursion
Résumé
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of spectral Darboux coordinates on the moduli space of meromorphic -connections on and argue that the topological recursion produces a 2g-parameter family of associated tau functions, where 2g is the dimension of the moduli space considered. We apply this procedure to the 6 Painlevé equations which correspond to and consider a example.
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