q-Painlevé equations on cluster Poisson varieties via toric geometry

• Yuma Mizuno ^[1]
  1. [1] Department of Mathematics and Informatics, Faculty of Science, Japan
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, págs. 1-37
• Idioma: inglés
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• Resumen

  • We provide a relation between the geometric framework for q-Painlevé equations and cluster Poisson varieties by using toric models of rational surfaces associated with qPainlevé equations. We introduce the notion of seeds of q-Painlevé type by the negative semi-definiteness of symmetric bilinear forms associated with seeds, and classify the mutation equivalence classes of these seeds. This classification coincides with the classification of q-Painlevé equations given by Sakai. We realize q-Painlevé systems as automorphisms on cluster Poisson varieties associated with seeds of q-Painlevé type.