{"paper":{"title":"On Grothendieck's construction of Teichm\\\"uller space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA), Lizhen Ji, Norbert A'Campo","submitted_at":"2016-03-07T19:49:07Z","abstract_excerpt":"In his 1944 paper Ver\\\"anderliche Riemannsche Fl\\\"achen , Teichm\\\"uller defined a structure of complex manifold on the set of isomorphism classes of marked closed Riemann surfaces of genus g. The complex manifold he obtained is the space called today Teichm\\\"uller space. In the same paper, Teichm\\\"uller introduced the so-called universal Teichm\\\"uller curve -- a space over Teichm\\\"uller space where the fiber above each point is a Riemann surface representing that point. In fact, Teichm\\\"uller proved the existence of the Teichm\\\"uller curve as a space of Riemann surfaces parametrized by an anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02229","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"}