{"paper":{"title":"Orbifold points on Prym-Teichm\\\"{u}ller curves in genus four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"David Torres-Teigell, Jonathan Zachhuber","submitted_at":"2016-09-01T08:35:00Z","abstract_excerpt":"For each discriminant $D>1$, McMullen constructed the Prym-Teichm\\\"uller curves $W_D(4)$ and $W_D(6)$ in $\\mathcal{M}_{3}$ and $\\mathcal{M}_{4}$, which constitute one of the few known infinite families of geometrically primitive Teichm\\\"{u}ller curves. In the present paper, we determine for each $D$ the number and type of orbifold points on $W_D(6)$. These results, together with a previous result of the two authors in the genus $3$ case and with results of Lanneau-Nguyen and M\\\"oller, complete the topological characterisation of all Prym-Teichm\\\"uller curves and determine their genus.\n  The st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00144","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"}