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In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0.Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by Enriques as an answer to a question discussed by about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by Reye are also examples of Enriques surfaces.

Attributes	Values
rdf:type	yago:WikicatComplexSurfaces yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatAlgebraicSurfaces
rdfs:label	Enriques surface (en) エンリケス曲面 (ja)
rdfs:comment	数学では、エンリケス曲面(Enriques surfaces)は、不正則数 q = 0 で標準ラインバンドル K が非自明であるが、二乗すると自明となるような代数曲面である。エンリケス曲面は、みな射影的であり（従って複素数体上ではケーラー的であり）、種数 0 の楕円曲面である。標数が 2 ではない体上では、エンリケス曲面はK3曲面を不動点のない位数 2 の群で割った商であり、その理論は代数的K3曲面の理論に似ている。エンリケス曲面は最初にで詳細に研究された。で、エンリケスの研究に先立ち導入されたレーイ合同(Reye congruences)のいくつかもまたエンリケス曲面の例である。エンリケス曲面は他の体上でも定義される。標数が 2 でない体上で、は理論が複素数上の理論と同じであることが示された。標数が 2 の体上では、定義が変更され、2つの新しい族が存在し、特異エンリケス曲面、超特異エンリケス曲面と呼ばれ、に記載されている。. (ja) In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0.Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by Enriques as an answer to a question discussed by about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by Reye are also examples of Enriques surfaces. (en)
dcterms:subject	Algebraic surfaces Complex surfaces Birational geometry
Wikipage page ID	3094760 (xsd:integer)
Wikipage revision ID	1080701960 (xsd:integer)
Link from a Wikipage to another Wikipage	Enriques–Kodaira classification Algebraic surface Betti number Inventiones Mathematicae Complex number Mathematics Elliptic surface Genus (mathematics) Fundamental group Automorphism Field (mathematics) Group (mathematics) Group action Tetrahedron Algebraic surfaces Complex surfaces Birational geometry Characteristic (algebra) K3 surface Homogeneous polynomial Group isomorphism Order (group theory) Unimodular lattice Plurigenus Canonical line bundle Supersingular variety List of algebraic surfaces dbr:Mem._Soc._Ital._Delle_Scienze
Link from a Wikipage to an external page	$http://www.math.biu.ac.il/~leyenson/library.classical-algebraic-geometry/self-scanned/enriques/enriques.le-superficie-algebriche.1949.300dpi.djvu$ https://archive.org/details/diegeometrieder01reyegoog https://dash.harvard.edu/bitstream/handle/1/3612776/Mumford_EnriquesClassIII.pdf%3Fsequence=3 http://www.math.lsa.umich.edu/~idolga/Kyoto13.pdf%7Cyear=2016
sameAs	Enriques surface Enriques surface Enriques surface Enriques surface Enriques surface
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Dead_link dbt:Harvtxt dbt:ISBN dbt:Harvs dbt:Hodge_diamond
bot	InternetArchiveBot (en)
date	September 2017 (en)
fix-attempted	yes (en)
has abstract	In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q = 0 and the canonical line bundle K is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex numbers) and are elliptic surfaces of genus 0.Over fields of characteristic not 2 they are quotients of K3 surfaces by a group of order 2 acting without fixed points and their theory is similar to that of algebraic K3 surfaces. Enriques surfaces were first studied in detail by Enriques as an answer to a question discussed by about whether a surface with q = pg = 0 is necessarily rational, though some of the Reye congruences introduced earlier by Reye are also examples of Enriques surfaces. Enriques surfaces can also be defined over other fields.Over fields of characteristic other than 2, showed that the theory is similar to that over the complex numbers. Over fields of characteristic 2 the definition is modified, and there are two new families, called singular and supersingular Enriques surfaces, described by . These two extra families are related to the two non-discrete algebraic group schemes of order 2 in characteristic 2. (en) 数学では、エンリケス曲面(Enriques surfaces)は、不正則数 q = 0 で標準ラインバンドル K が非自明であるが、二乗すると自明となるような代数曲面である。エンリケス曲面は、みな射影的であり（従って複素数体上ではケーラー的であり）、種数 0 の楕円曲面である。標数が 2 ではない体上では、エンリケス曲面はK3曲面を不動点のない位数 2 の群で割った商であり、その理論は代数的K3曲面の理論に似ている。エンリケス曲面は最初にで詳細に研究された。で、エンリケスの研究に先立ち導入されたレーイ合同(Reye congruences)のいくつかもまたエンリケス曲面の例である。エンリケス曲面は他の体上でも定義される。標数が 2 でない体上で、は理論が複素数上の理論と同じであることが示された。標数が 2 の体上では、定義が変更され、2つの新しい族が存在し、特異エンリケス曲面、超特異エンリケス曲面と呼ばれ、に記載されている。. (ja)
prov:wasDerivedFrom	wikipedia-en:Enriques_surface?oldid=1080701960&ns=0
page length (characters) of wiki page	8288 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Enriques_surface
is Link from a Wikipage to another Wikipage of	Enriques–Kodaira classification List of algebraic geometry topics List of complex and algebraic surfaces David Mumford Algebraic surface List of manifolds Elliptic surface Calabi–Yau manifold Irregularity of a surface Rational surface Federigo Enriques Kodaira surface Theodor Reye K3 surface Enriques surfaces Kodaira dimension Semiorthogonal decomposition Rokhlin's theorem Quasi-Enriques surface Quasi Enriques surface Reye congruence Supersingular Enriques surface Singular Enriques surface
is Wikipage redirect of	Enriques surfaces Quasi-Enriques surface Quasi Enriques surface Reye congruence Supersingular Enriques surface Singular Enriques surface
is known for of	Federigo Enriques
is known for of	Federigo Enriques
is foaf:primaryTopic of	wikipedia-en:Enriques_surface

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