{"paper":{"title":"Geometric Aspects of Painlev\\'e Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Kenji Kajiwara, Masatoshi Noumi, Yasuhiko Yamada","submitted_at":"2015-09-28T03:47:50Z","abstract_excerpt":"In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlev\\'e equations, with a particular emphasis on the discrete Painlev\\'e equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on $\\mathbb{P}^1\\times\\mathbb{P}^1$ and classified according to the degeration of points. We give a systematic description of the equations and their various properties, such as affine Weyl group symmetries, hypergeomtric solutions and L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08186","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}