{"paper":{"title":"Normalization of complex analytic spaces from a global viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabrizio Broglia, Francesca Acquistapace, Jos\\'e F. Fernando","submitted_at":"2017-10-10T10:24:31Z","abstract_excerpt":"In this work we study some algebraic and topological properties of the ring ${\\mathcal O}(X^\\nu)$ of global analytic functions of the normalization $(X^\\nu,{\\mathcal O}_{X^\\nu})$ of a reduced complex analytic space $(X,{\\mathcal O}_X)$. If $(X,{\\mathcal O}_X)$ is a Stein space, we characterize ${\\mathcal O}(X^\\nu)$ in terms of the (topological) completion of the integral closure $\\overline{{\\mathcal O}(X)}^\\nu$ of the ring ${\\mathcal O}(X)$ of global holomorphic functions on $X$ (inside its total ring of fractions) with respect to the usual Fr\\'echet topology of $\\overline{{\\mathcal O}(X)}^\\nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03497","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"}