{"paper":{"title":"Q.E.D. for algebraic varieties","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fabrizio Catanese (Universitaet Bayreuth)","submitted_at":"2005-09-30T15:24:39Z","abstract_excerpt":"We introduce a new equivalence relation, denoted by $A.Q.E.D.$ (= Algebraic-Quasi-\\'Etale- Deformation) for complete algebraic varieties with canonical singularities: it is generated by birational equivalence, by flat algebraic deformations, and by quasi-\\'etale morphisms, i.e., morphisms which are unramified in codimension $1$. $\\C$-Q.E.D is the similar relation for compact complex manifolds and spaces. By a recent theorem of Siu dimension and Kodaira dimension are invariants for $A.Q.E.D.$. The question whether conversely two algebraic varieties of the same dimension and with the same Kodair"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509725","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"}