{"paper":{"title":"Deformation types of real and complex manifolds","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fabrizio M.E. Catanese (University of Bayreuth)","submitted_at":"2001-11-22T15:08:30Z","abstract_excerpt":"The Leit-Faden of the article (which is partially a survey) is a negative answer to the question whether, for a compact complex manifold which is a $K(\\pi, 1)$ the diffeomorphism type determines the deformation type. We show that a deformation in the large of complex tori is again a complex torus, and then that the same holds for products of a torus with a curve of genus $g\\geq 2$. Together with old results of Blanchard, Calabi, and Sommese, who showed the existence of non K\\\"ahler complex structures on the product of a curve with a two dimensional complex torus, this gives the first counterex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0111245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0111245/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}