{"paper":{"title":"On Yau's theorem for effective orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mitchell Faulk","submitted_at":"2017-10-31T16:17:50Z","abstract_excerpt":"In 1978, Yau confirmed a conjecture due to Calabi stating the existence of K\\\"ahler metrics with prescribed Ricci forms on compact K\\\"ahler manifolds. A version of this statement for effective orbifolds can be found in the literature. In this expository article, we provide details for a proof of this orbifold version of the statement by adapting Yau's original continuity method to the setting of effective orbifolds in order to solve a Monge-Amp\\`ere equation. We then outline how to obtain K\\\"ahler-Einstein metrics on orbifolds with $c_1(\\mathcal{X}) < 0$ by solving a slightly different Monge-A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11561","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"}