About: Normal scheme

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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 .

Attributes	Values
rdf:type	Thing
rdfs:label	Normale Varietät (de) 정규 스킴 (ko) Normal scheme (en)
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)
foaf:depiction
dcterms:subject	Algebraic geometry Scheme theory
Wikipage page ID	2629423 (xsd:integer)
Wikipage revision ID	1015468261 (xsd:integer)
Link from a Wikipage to another Wikipage	Noether normalization lemma Resolution of singularities Integral domain Integrally closed domain Topologically stratified space Local ring Affine variety Algebraic curve Algebraic geometry Algebraic varieties Graduate Texts in Mathematics Proper morphism Regular function Algebraic geometry Birational geometry Scheme theory Field of fractions Glossary of scheme theory Integral closure Rational normal curve Rational normal scroll Scheme (mathematics) Finite morphism Linearly normal Springer-Verlag Reduced scheme
sameAs	Normal scheme Normal scheme Normal scheme Normal scheme Normal scheme
dbp:wikiPageUsesTemplate	dbt:Authority_control dbt:Citation dbt:Harvtxt dbt:Reflist dbt:Harvs dbt:Hartshorne_AG
thumbnail	wiki-commons:Special:FilePath/Newtonsche_Knoten.png?width=300
authorlink	Oscar Zariski (en)
last	Zariski (en)
year	1939 (xsd:integer)
loc	section III (en)
has 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)
prov:wasDerivedFrom	wikipedia-en:Normal_scheme?oldid=1015468261&ns=0
page length (characters) of wiki page	7254 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Normal_scheme
is Link from a Wikipage to another Wikipage of	Minimal prime ideal Normal algebraic variety Normal schemes Normal variety Degeneration (algebraic geometry) Integral element Integrally closed domain Nef line bundle Normal Normalization of an algebraic variety Geometric genus Glossary of algebraic geometry Glossary of classical algebraic geometry Monomial ideal Fundamental group scheme Affine variety Gorenstein scheme Hilbert's fourteenth problem Moduli of algebraic curves Picard group Rational normal curve Rational normal scroll Rational singularity Torus action Smooth scheme Reflexive sheaf
is Wikipage redirect of	Normal algebraic variety Normal schemes Normal variety Normalization of an algebraic variety
is Wikipage disambiguates of	Normal
is foaf:primaryTopic of	wikipedia-en:Normal_scheme

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