About: Irregularity of a surface

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In mathematics, the irregularity of a complex surface X is the Hodge number , usually denoted by q. The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety, which is the same in characteristic 0 but can be smaller in positive characteristic. For a complex analytic manifold X of general dimension, the Hodge number is called the irregularity of , and is denoted by q.

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rdf:type	yago:WikicatComplexSurfaces yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 chemical compound yago:Surface104362025 yago:Whole100003553 yago:WikicatAlgebraicSurfaces
rdfs:label	Irregularity of a surface (en) 曲面の不正則数 (ja)
rdfs:comment	数学では、複素曲面の不正則数(irregularity)とは、ホッジ数 h0,1 = dim H1(OX) のことをいい、通常 q で表す(Wolf P. Barth, Klaus Hulek & Chris A.M. Peters et al. )。代数曲面の不正則数は、このホッジ数として定義され、ピカール多様体の次元としても定義でき、標数が 0 のときは同じ値をとるが、正の標数のときはより小さくなることがある。「不正則数」という名称は、最初に詳細に研究された曲面である P3 に埋め込まれたなめらかな複素曲面に対して、不正則数がゼロになるという事実からくる。不正則数は、より複雑な曲面の幾何種数と算術種数の差 pg − pa を測る新しい「補正」項として現れる。曲面は不正則数がゼロであるか否かに従い、正則、不正則と呼ばれることがある。一般次元の複素解析多様体 X に対し、ホッジ数 h0,1 = dim H1(OX) のことを、不正則数 q と言う。 (ja) In mathematics, the irregularity of a complex surface X is the Hodge number , usually denoted by q. The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety, which is the same in characteristic 0 but can be smaller in positive characteristic. For a complex analytic manifold X of general dimension, the Hodge number is called the irregularity of , and is denoted by q. (en)
dcterms:subject	Algebraic surfaces Complex surfaces
Wikipage page ID	22857258 (xsd:integer)
Wikipage revision ID	1054218918 (xsd:integer)
Link from a Wikipage to another Wikipage	Enriques surface Geometric genus Arithmetic genus Alexander Grothendieck Henri Poincaré Algebraic surfaces Complex surfaces Albanese variety Jun-Ichi Igusa Pierre Cartier (mathematician) Kähler manifold Hodge number Positive characteristic Kähler surface Bockstein operation Picard variety Complex surface
sameAs	Irregularity of a surface Irregularity of a surface Irregularity of a surface Irregularity of a surface Irregularity of a surface
has abstract	In mathematics, the irregularity of a complex surface X is the Hodge number , usually denoted by q. The irregularity of an algebraic surface is sometimes defined to be this Hodge number, and sometimes defined to be the dimension of the Picard variety, which is the same in characteristic 0 but can be smaller in positive characteristic. The name "irregularity" comes from the fact that for the first surfaces investigated in detail, the smooth complex surfaces in P3, the irregularity happens to vanish. The irregularity then appeared as a new "correction" term measuring the difference of the geometric genus and the arithmetic genus of more complicated surfaces. Surfaces are sometimes called regular or irregular depending on whether or not the irregularity vanishes. For a complex analytic manifold X of general dimension, the Hodge number is called the irregularity of , and is denoted by q. (en) 数学では、複素曲面の不正則数(irregularity)とは、ホッジ数 h0,1 = dim H1(OX) のことをいい、通常 q で表す(Wolf P. Barth, Klaus Hulek & Chris A.M. Peters et al. )。代数曲面の不正則数は、このホッジ数として定義され、ピカール多様体の次元としても定義でき、標数が 0 のときは同じ値をとるが、正の標数のときはより小さくなることがある。「不正則数」という名称は、最初に詳細に研究された曲面である P3 に埋め込まれたなめらかな複素曲面に対して、不正則数がゼロになるという事実からくる。不正則数は、より複雑な曲面の幾何種数と算術種数の差 pg − pa を測る新しい「補正」項として現れる。曲面は不正則数がゼロであるか否かに従い、正則、不正則と呼ばれることがある。一般次元の複素解析多様体 X に対し、ホッジ数 h0,1 = dim H1(OX) のことを、不正則数 q と言う。 (ja)
gold:hypernym	H
prov:wasDerivedFrom	wikipedia-en:Irregularity_of_a_surface?oldid=1054218918&ns=0
page length (characters) of wiki page	6945 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Irregularity_of_a_surface
is Link from a Wikipage to another Wikipage of	Enriques–Kodaira classification List of algebraic geometry topics Algebraic surface Irregular Noether inequality Glossary of classical algebraic geometry Hairy ball theorem Differential of the first kind Regular Albanese variety K3 surface Burniat surface Kodaira dimension Surface of general type Irregular surface
is Wikipage redirect of	Irregular surface
is Wikipage disambiguates of	Irregular Regular
is foaf:primaryTopic of	wikipedia-en:Irregularity_of_a_surface

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