{"paper":{"title":"Some examples due to H. Hironaka","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Barlet","submitted_at":"2015-01-06T10:28:34Z","abstract_excerpt":"The aim of this paper is to explain the construction by H. Hironaka [H.61] of a holomorphic (in fact \"algebraic\") family of compact complex manifolds  parametrized by $\\C$ such for all $s \\in \\C\\setminus \\{0\\}$ the fiber is projective, but such that the fiber at the origin in non k{\\\"a}hlerian, to mathematicians which are not algebraic geometers. We also explain why it is not possible to make in the same way such  an example with fiber at $0$ a simpler example of non k{\\\"a}hlerian Moishezon manifold which is also due to H. Hironaka (see section 5)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01129","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"}