{"paper":{"title":"A Riemann--Hilbert approach to Painlev\\'e IV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaap Top, Marius van der Put","submitted_at":"2012-07-18T10:53:45Z","abstract_excerpt":"This paper applies methods of Van der Put and Van derPut-Saito to the fourth Painlev\\'e equation. One obtains a Riemann--Hilbert correspondence between moduli spaces of rank two connections on $\\mathbb{P}^1$ and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto--Painlev\\'e varieties and the Painlev\\'e property follows. For an explicit computation of the full group of B\\\"acklund transformations, rank three connections on $\\mathbb{P}^1$ are introduced, inspired by the symmetric form for ${\\rm PIV}$ as was studied by M. Noumi and Y. Yamada."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4335","kind":"arxiv","version":1},"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"}