\(q\)-Painlevé equations on cluster Poisson varieties via toric geometry

DOI10.1007/s00029-023-00906-2arXiv2008.11219OpenAlexW3176334293MaRDI QIDQ6186433

Yuma Mizuno

Publication date: 2 February 2024

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11219

zbMATH Keywords

toric geometrycluster algebras\(q\)-Painlevé systems

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Difference equations, scaling ((q)-differences) (39A13) Cluster algebras (13F60)

Cites Work

• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Cluster integrable systems, \(q\)-Painlevé equations and their quantization
• A \(q\)-analog of the sixth Painlevé equation
• Classification of rank 2 cluster varieties
• Cluster algebras I: Foundations
• Cluster automorphisms
• Canonical bases for cluster algebras
• Birational geometry of cluster algebras
• Cluster ensembles, quantization and the dilogarithm
• MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS
• Moduli of surfaces with an anti-canonical cycle
• Dimers and cluster integrable systems
• On cluster theory and quantum dilogarithm identities
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