{"paper":{"title":"Complex affine spheres and a Bers theorem for SL(3,C)","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV","math.GT"],"primary_cat":"math.DG","authors_text":"Christian El Emam, Nathaniel Sagman","submitted_at":"2024-06-21T16:31:49Z","abstract_excerpt":"For $S$ a closed surface of genus at least $2$, let $\\mathrm{Hit}_3(S)$ be the Hitchin component of representations to $\\mathrm{SL}(3,\\mathbb{R}),$ equipped with the Labourie-Loftin complex structure. We construct a mapping class group equivariant holomorphic map from a large open subset of $\\mathrm{Hit}_3(S)\\times \\overline{\\mathrm{Hit}_3(S)}$ to the $\\mathrm{SL}(3,\\mathbb{C})$-character variety that restricts to the identity on the diagonal and to Bers' simultaneous uniformization on $\\mathrm{T}(S)\\times \\overline{\\mathrm{T}(S)}$. The open subset contains $\\mathrm{Hit}_3(S)\\times \\overline{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.15287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}