{"paper":{"title":"Conformally K\\\"ahler, Einstein-Maxwell Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gideon Maschler, Vestislav Apostolov","submitted_at":"2015-12-20T16:06:17Z","abstract_excerpt":"On a given compact complex manifold or orbifold $(M,J)$, we study the existence of Hermitian metrics $\\tilde g$ in the conformal classes of K\\\"ahler metrics on $(M,J)$, such that the Ricci tensor of $\\tilde g$ is of type $(1,1)$ with respect to the complex structure, and the scalar curvature of $\\tilde g$ is constant. In real dimension $4$, such Hermitian metrics provide a Riemannian counter-part of the Einstein--Maxwell (EM) equations in general relativity, and have been recently studied in \\cite{ambitoric1, LeB0, LeB, KTF}. We show how the existence problem of such Hermitian metrics (which w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06391","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"}