{"paper":{"title":"Deformation of Okamoto-Painlev\\'e Pairs and Painlev\\'e equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Faculty of Science, Hitomi Terajima (Department of Mathematics, Japan), Kobe, Kobe University, Masa-Hiko Saito, Taro Takebe","submitted_at":"2000-06-05T04:50:57Z","abstract_excerpt":"In this paper, we introduce the notion of generalized rational Okamoto-Painlev\\'e pair (S, Y) by generalizing the notion of the spaces of initial conditions of Painlev\\'e equations. After classifying those pairs, we will establish an algebro-geometric approach to derive the Painlev\\'e differential equations from the deformation of Okamoto-Painlev\\'e pairs by using the local cohomology groups. Moreover the reason why the Painlev\\'e equations can be written in Hamiltonian systems is clarified by means of the holomorphic symplectic structure on S - Y. Hamiltonian structures for Okamoto-Painlev\\'e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0006026","kind":"arxiv","version":2},"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"}