{"paper":{"title":"Autonomous limit of 4-dimensional Painlev\\'e-type equations and degeneration of curves of genus two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akane Nakamura","submitted_at":"2015-05-05T06:13:50Z","abstract_excerpt":"Higher dimensional analogs of the Painlev\\'e equations have been proposed from various aspects. In recent studies, 4-dimensional analogs of the Painlev\\'e equations were classified into 40 types. The aim of the present paper is to geometrically characterize these 40 types of equations. For this purpose, we study the autonomous limit of these equations and degeneration of their spectral curves. We obtain two functionally independent conserved quantities $H_1$ and $H_2$ for each system. We construct fibrations whose fiber at a general point $h_i $ is the spectral curve of the system with $H_i=h_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00885","kind":"arxiv","version":3},"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"}