{"paper":{"title":"Isomonodromic deformation of Lam\\'e connections, Painlev\\'e VI equation and Okamoto symetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Frank Loray","submitted_at":"2014-10-18T16:22:00Z","abstract_excerpt":"A Lam\\'e connection is a logarithmic $\\mathrm{sl}(2,\\mathbb C)$-connection $(E,\\nabla)$ over an elliptic curve $X:\\{y^2=x(x-1)(x-t)\\}$, $t\\not=0,1$, having a single pole at infinity. When this connection is irreducible, we show that it is invariant by the standart involution and can be pushed down as a logarithmic $\\mathrm{sl}(2,\\mathbb C)$-connection over $\\mathbb P^1$ with poles at $0$, $1$, $t$ and $\\infty$. Therefore, the isomonodromic deformation $(E_t,\\nabla_t)$ of an irreducible Lam\\'e connection, when the elliptic curve $X_t$ varry in the Legendre family, is parametrized by a solution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4976","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"}