| dbo:abstract |
In der algebraischen Geometrie, einem Teilgebiet der Mathematik, sind normale Varietäten algebraische Varietäten mit nur milden Singularitäten. Der Begriff wurde von Oscar Zariski im Zusammenhang mit seiner rein algebraischen, auf kommutativer Algebra beruhenden Grundlegung der algebraischen Geometrie und seinen Arbeiten zur eingeführt. (de) In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. A variety X over a field is normal if and only if every finite birational morphism from any variety Y to X is an isomorphism. Normal varieties were introduced by Zariski . (en) 대수기하학에서 정규 스킴(正規scheme, 영어: normal scheme)은 모든 국소환이 정수적으로 닫힌 정역인 스킴이다. (ko) |
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| dbp:authorlink |
Oscar Zariski (en) |
| dbp:last |
Zariski (en) |
| dbp:loc |
section III (en) |
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1939 (xsd:integer) |
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dbc:Algebraic_geometry dbc:Scheme_theory |
| rdf:type |
owl:Thing |
| rdfs:comment |
In der algebraischen Geometrie, einem Teilgebiet der Mathematik, sind normale Varietäten algebraische Varietäten mit nur milden Singularitäten. Der Begriff wurde von Oscar Zariski im Zusammenhang mit seiner rein algebraischen, auf kommutativer Algebra beruhenden Grundlegung der algebraischen Geometrie und seinen Arbeiten zur eingeführt. (de) In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. An affine variety X (understood to be irreducible) is normal if and only if the ring O(X) of regular functions on X is an integrally closed domain. A variety X over a field is normal if and only if every finite birational morphism from any variety Y to X is an isomorphism. Normal varieties were introduced by Zariski . (en) 대수기하학에서 정규 스킴(正規scheme, 영어: normal scheme)은 모든 국소환이 정수적으로 닫힌 정역인 스킴이다. (ko) |
| rdfs:label |
Normale Varietät (de) 정규 스킴 (ko) Normal scheme (en) |
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