{"paper":{"title":"On volume preserving complex structures on real tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Fabrizio Catanese (Universitaet Bayreuth), Keiji Oguiso (Osaka University), Thomas Peternell (Universitaet Bayreuth)","submitted_at":"2009-12-29T14:37:28Z","abstract_excerpt":"A basic problem in the classification theory of compact complex manifolds is to give simple characterizations of complex tori. It is well known that a compact K\\\"ahler manifold $X$ homotopically equivalent to a a complex torus is biholomorphic to a complex torus.\n  The question whether a compact complex manifold $X$ diffeomorphic to a complex torus is biholomorphic to a complex torus has a negative answer due to a construction by Blanchard and Sommese.\n  Their examples have however negative Kodaira dimension, thus it makes sense to ask the question whether a compact complex manifold $X$ with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5313","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"}