{"paper":{"title":"Spherical metrics with conical singularities on 2-spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Subhadip Dey","submitted_at":"2017-04-16T21:46:39Z","abstract_excerpt":"Suppose that $\\theta_1,\\theta_2,\\dots,\\theta_n$ are positive numbers and $n\\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical singularities of angles $2\\pi\\theta_1,2\\pi\\theta_2,\\dots,2\\pi\\theta_n$? A sufficient condition was obtained by Gabriele Mondello and Dmitri Panov (arXiv:1505.01994). We show that it is also necessary when we assume that $\\theta_1,\\theta_2,\\dots,\\theta_n \\not\\in \\mathbb{N}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04823","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"}