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Variants of Normality for Noetherian Schemes

Author(s): Kollar, Janos

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Abstract: This note presents a uniform treatment of normality and three of its variants-topological, weak and seminormality-for Noetherian schemes. The key is to define these notions for pairs Z subset of X consisting of a (not necessarily reduced) scheme X and a closed, nowhere dense subscheme Z. An advantage of the new definitions is that, unlike the usual absolute ones, they are preserved by completions. This shortens some of the proofs and leads to more general results.
Publication Date: 2016
Electronic Publication Date: 2016
Citation: Kollar, Janos. (2016). Variants of Normality for Noetherian Schemes. PURE AND APPLIED MATHEMATICS QUARTERLY, 12 (1 - 31
ISSN: 1558-8599
EISSN: 1558-8602
Pages: 1 - 31
Type of Material: Journal Article
Version: Author's manuscript

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