{"paper":{"title":"Note on algebro-geometric solutions to triangular Schlesinger systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.AG","authors_text":"Vasilisa Shramchenko, Vladimir Dragovic","submitted_at":"2016-04-06T21:50:50Z","abstract_excerpt":"We construct algebro-geometric upper triangular solutions of rank two Schlesinger systems. Using these solutions we derive two families of solutions to the sixth Painlev\\'e equation with parameters $({1}/{8}, -{1}/{8}, {1}/{8}, {3}/{8})$ expressed in simple forms using periods of differentials on elliptic curves. Similarly for every integer $n$ different from $0$ and $-1$ we obtain one family of solutions to the sixth Painlev\\'e equation with parameters $(\\frac{9n^2+12n+4}{8}, -\\frac{n^2}{8}, \\frac{n^2}{8}, \\frac{4-n^2}{8})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01820","kind":"arxiv","version":5},"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"}