About: Ample line bundle

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In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to having many global sections. Understanding the ample line bundles on a given variety X amounts to understanding the different ways of mapping X into projective space. In view of the correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of an ample divisor.

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rdf:type	yago:WikicatVectorBundles yago:Abstraction100002137 yago:Collection107951464 yago:Group100031264 yago:Package108008017
rdfs:label	Ample line bundle (en) 豊富な直線束 (ja) 풍부한 가역층 (ko)
rdfs:comment	대수기하학에서 풍부한 가역층(豐富한可逆層, 영어: ample invertible sheaf)은 그 거듭제곱의 단면들을 사영 공간의 동차 좌표로 간주하여 대수다양체를 사영 공간에 매장시킬 수 있는 가역층이다. 복소수체 위에서, 이는 가역층의 천 특성류가 켈러 구조로 표현됨을 뜻한다. (ko) 代数幾何学では、非常に豊富な直線束(very ample line bundle)は、基礎となる代数多様体や多様体 M から射影空間への埋め込みを行う設定に充分な大域的切断があるバンドルのことを言う。豊富な直線束(ample line bundle)はバンドルのある正のべきが非常に豊富となるときを言う。大域的に生成された層(globally generated sheaves)とは、射影空間への射を定義することに充分な切断を持つ層のことを言う。 (ja) In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to having many global sections. Understanding the ample line bundles on a given variety X amounts to understanding the different ways of mapping X into projective space. In view of the correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of an ample divisor. (en)
dcterms:subject	Vector bundles Geometry of divisors Algebraic geometry
Wikipage page ID	1186896 (xsd:integer)
Wikipage revision ID	1080538653 (xsd:integer)
Link from a Wikipage to another Wikipage	American Journal of Mathematics Projective space Quasi-coherent sheaf Quasi-compact Robin Hartshorne David Mumford Algebraic geometry of projective spaces Algebraic space Algebraically closed field Annals of Mathematics Holomorphic vector bundle Vector space Degree of an algebraic variety Invertible sheaf Affine scheme Néron–Severi group Quasi-affine morphism Complex number Genus (mathematics) Nef line bundle Noetherian ring Pullback bundle Quasi-separated morphism Closure (topology) Elliptic curve Branched covering Morphism of algebraic varieties Cone of curves Projective scheme Closed immersion Commutative ring Complex geometry Matsusaka's big theorem Publications Mathématiques de l'IHÉS C. S. Seshadri Vector bundles Divisorial scheme Line bundle Linear combination Sheaf of modules Stein manifold Alexander Grothendieck Algebraic Geometry (book) Algebraic curve Algebraic geometry Field (mathematics) Birational Fano variety Kodaira embedding theorem Kodaira vanishing theorem Lefschetz hyperplane theorem Faisceaux algébriques cohérents Projective variety Proper morphism Rational point Henri Cartan Irreducible component Jean-Pierre Serre Hyperelliptic curve Hyperplane Geometry of divisors Algebraic geometry Chern class Birational geometry Blowing up Codimension Coherent sheaf Coherent sheaf cohomology Homogeneous polynomial Picard group Boris Moishezon Scheme-theoretic fiber Tensor product of line bundles Canonical bundle Rational normal curve Real number Scheme (mathematics) Section (fiber bundle) Vector bundle Zariski topology Linear systems of divisors Finite morphism Algebraic vector bundle Smooth scheme

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