{"paper":{"title":"$\\partial\\bar{\\partial}$-complex symplectic and Calabi-Yau manifolds: Albanese map, deformations and period maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Adriano Tomassini, Andrea Cattaneo, Ben Anthes, S\\\"onke Rollenske","submitted_at":"2017-11-14T14:30:22Z","abstract_excerpt":"Let $X$ be a compact complex manifold with trivial canonical bundle and satisfying the $\\partial\\bar{\\partial}$-Lemma. We show that the Kuranishi space of $X$ is a smooth universal deformation and that small deformations enjoy the same properties as $X$. If, in addition, $X$ admits a complex symplectic form, then the local Torelli theorem holds and we obtain some information about the period map.\n  We clarify the structure of such manifolds a little by showing that the Albanese map is a surjective submersion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05107","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"}