About: Elliptic surface

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In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.) This is equivalent to the generic fiber being a smooth curve of genus one. This follows from proper base change.

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rdf:type	Thing bone yago:WikicatComplexSurfaces yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:Surface104362025 yago:Whole100003553 yago:WikicatAlgebraicSurfaces
rdfs:label	Elliptic surface (en) 타원 곡면 (ko) 楕円曲面 (ja)
rdfs:comment	数学では、楕円曲面（だえんきょくめん、英: elliptic surface）は楕円ファイバーを持つ曲面であり、言い換えると、曲面からの代数曲線への連結な固有射が、ほとんどの点上のファイバーを楕円曲線とするような曲面である。ファイバーが楕円曲線とならない点を特異ファイバー (singular fibers) と呼び、小平邦彦により分類された。弦理論の脈絡では、楕円ファイバーも特異ファイバーも (F-theory) を使う記述にとっても重要である。楕円曲面は、曲面の興味深い例の多くを含む、曲面の大きなクラスで、複素幾何学の観点からも滑らかな(smooth) 4次元多様体の理論の観点からも、比較的良く理解されている。楕円曲面は代数体上の楕円曲線に似ている（つまり、類似している）。 (ja) ( 비슷한 이름의 타원면에 관해서는 해당 문서를 참조하십시오.) 대수기하학에서 타원 곡면(橢圓曲面, 영어: elliptic surface)은 거의 모든 곳에서 타원 곡선을 올로 하는 올다발이 주어진 곡면이다. (ko) In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.) This is equivalent to the generic fiber being a smooth curve of genus one. This follows from proper base change. (en)
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dcterms:subject	Algebraic surfaces Complex surfaces Birational geometry Mathematical classification systems
Wikipage page ID	3073462 (xsd:integer)
Wikipage revision ID	1112932971 (xsd:integer)
Link from a Wikipage to another Wikipage	Enriques surface Enriques–Kodaira classification Determinant Dynkin diagram Mathematics Genus (mathematics) Tate's algorithm Elliptic-curve cryptography Enriques-Kodaira classification Monodromy Conjugacy class André Néron Calabi–Yau manifold String theory Complex manifold Yujiro Kawamata Picard group Publications Mathématiques de l'IHÉS Dolgachev surface Algebraic curve 4-manifold Number field Oxford University Press Kenji Ueno Kodaira surface Proper morphism J-invariant ADE classification Algebraic surfaces Complex surfaces Birational geometry Birkhäuser Homology (mathematics) Regular scheme Mordell-Weil theorem Smoothness Picard group Springer Nature Mathematical classification systems Kodaira dimension Kunihiko Kodaira Canonical bundle Section (fiber bundle) Shioda modular surface F-theory Potential good reduction Smooth scheme Proper base change theorem Divisor class group Zero matrix List of simple Lie groups Affine Cartan matrix Néron minimal model Holomorphic Euler characteristic

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