{"paper":{"title":"Complex symplectic structures and the $\\partial \\bar{\\partial}$-lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Adriano Tomassini, Andrea Cattaneo","submitted_at":"2016-12-24T13:53:22Z","abstract_excerpt":"In this paper we study complex symplectic manifolds, i.e., compact complex manifolds $X$ which admit a holomorphic $(2, 0)$-form $\\sigma$ which is $d$-closed and non-degenerate, and in particular the Beauville-Bogomolov-Fujiki quadric $Q_\\sigma$ associated to them. We will show that if X satisfies the $\\partial \\bar{\\partial}$-lemma, then $Q_\\sigma$ is smooth if and only if $h^{2,0}(X) = 1$ and is irreducible if and only if $h^{1,1}(X) > 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08183","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"}