{"paper":{"title":"On the existence of holomorphic curves in compact quotients of $\\mathrm{SL}(2,\\mathbb C)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Lynn Heller, Sebastian Heller, Sorin Dumitrescu","submitted_at":"2021-12-06T15:58:37Z","abstract_excerpt":"We prove the existence of a pair $(\\Sigma ,\\, \\Gamma)$, where $\\Sigma$ is a compact Riemann surface with $\\text{genus}(\\Sigma)\\, \\geq\\, 2$, and $\\Gamma\\, \\subset\\, {\\mathrm SL}(2, \\mathbb C)$ is a cocompact lattice, such that there is a generically injective holomorphic map $\\Sigma \\, \\longrightarrow\\, {\\mathrm SL}(2, \\mathbb C)/\\Gamma$. This gives an affirmative answer to a question raised by Huckleberry and Winkelmann \\cite{HW} and by Ghys \\cite{Gh}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.03131","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.03131/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"}