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Ample line bundle

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…

Criteria for ampleness of line bundles, Definitions & Introduction

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Overview

Introduction

Definitions

Examples/Non-examples

Criteria for ampleness of line bundles

Generalizations

Relative ampleness

General algebraic geometry

Ampleness in complex geometry

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Map overview Semantic statistics

Ample line bundle

Nodes107
Edges106
Triples31
Avg. degree1.98
Density0.018692
Components1

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Ample line bundle

Top relations

related to Examples/Non-examples · 11
Ample line bundle → Also, But, For, In, Let, More, On, So, The, Then, Therefore
related to Ample invertible sheaves on quasi-compact schemes · 5
Ample line bundle → Ample, Equivalently, For, Gamma, Let
related to Ample vector bundles · 5
Ample line bundle → Also, Chern, For, Robin Hartshorne, Several
related to Big line bundles · 5
Ample line bundle → Also, Finally, First, There, This
related to On proper schemes · 5
Ample line bundle → An, In, Often, The, When

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Important terminology

displaystyle line ample bundle projective mathcal every degree field positive proper scheme space morphism curve sections otimes basepoint-free bundles sheaf

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ample line bundlerelated to Ample invertible sheaves on quasi-compact schemesAmple0.60section
Ample line bundlerelated to Ample invertible sheaves on quasi-compact schemesLet0.60section
Ample line bundlerelated to Ample invertible sheaves on quasi-compact schemesFor0.60section
Ample line bundlerelated to Ample invertible sheaves on quasi-compact schemesGamma0.60section
Ample line bundlerelated to Ample invertible sheaves on quasi-compact schemesEquivalently0.60section
Ample line bundlerelated to Ample vector bundlesRobin Hartshorne0.60section
Ample line bundlerelated to Ample vector bundlesSeveral0.60section
Ample line bundlerelated to Ample vector bundlesFor0.60section
Ample line bundlerelated to Ample vector bundlesAlso0.60section
Ample line bundlerelated to Ample vector bundlesChern0.60section
Ample line bundlerelated to Big line bundlesThis0.60section
Ample line bundlerelated to Big line bundlesThere0.60section

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