{"paper":{"title":"The equation of the Kenyon-Smillie $(2,3,4)$-Teichm\\\"uller curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GT","authors_text":"Andr\\'e Kappes, Matteo Costantini","submitted_at":"2016-01-12T09:46:11Z","abstract_excerpt":"We compute the algebraic equation of the universal family over the Kenyon-Smillie $(2,3,4)$-Teichm\\\"uller curve and give a nice geometric description of the torsion map. Moreover, we re-prove independently that the found algebraic equation describes a Teichm\\\"uller curve by computing the Picard-Fuchs equation associated to the absolute cohomology bundle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02783","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"}