{"paper":{"title":"Holomorphic Deformations of Balanced Calabi-Yau $\\partial\\bar\\partial$-Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Dan Popovici","submitted_at":"2013-04-01T11:18:15Z","abstract_excerpt":"Given a compact complex $n$-fold $X$ satisfying the $\\partial\\bar\\partial$-lemma and supposed to have a trivial canonical bundle $K_X$ and to admit a balanced (=semi-K\\\"ahler) Hermitian metric $\\omega$, we introduce the concept of deformations of $X$ that are {\\bf co-polarised} by the balanced class $[\\omega^{n-1}]\\in H^{n-1,\\,n-1}(X,\\,\\C)\\subset H^{2n-2}(X,\\,\\C)$ and show that the resulting theory of balanced co-polarised deformations is a natural extension of the classical theory of K\\\"ahler polarised deformations in the context of Calabi-Yau or even holomorphic symplectic compact complex ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0331","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"}