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Affine variety

In algebraic geometry, an affine variety or affine algebraic variety is a certain kind of algebraic variety that can be described as a subset of an affine space.

Generalizations, Examples & Affine algebraic groups

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Overview

Introduction

Examples

Rational points

Singular points and tangent space

The Zariski topology

Geometry–algebra correspondence

Products of affine varieties

Morphisms of affine varieties

Structure sheaf

Serre's theorem on affineness

Affine algebraic groups

Generalizations

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Map overview Semantic statistics

Affine variety

Nodes97
Edges96
Triples50
Avg. degree1.98
Density0.020619
Components1

How this topic connects Entity context

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Affine variety

Top relations

related to Generalizations · 14
Affine variety → Affine, An, Any, Claim, Each, Gamma, Generalizing, If, Linear, More, Spec, Structure, The, This
related to Examples · 11
Affine variety → Algebraic, Examples, For, Hartogs, In, Its, Non-affine, On, See Spectrum, Similarly, The
related to Rational points · 8
Affine variety → For, It, Often, Q-rational, R-rational, That, The, This
related to Structure sheaf · 7
Affine variety → An, Equipped, Gamma, Given, It, Moreover, Since
related to Serre's theorem on affineness · 3
Affine variety → Cartan's, Serre, This
related to Singular points and tangent space · 3
Affine variety → JV, Let, The Jacobian
is a · 2
Affine variety → affine algebraic set which is not the union of two smaller algebraic sets, locally ringed space.Given an affine variety X with coordinate ring A
related to Affine algebraic groups · 1
Affine variety → An

Important terminology Word statistics

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Important terminology

affine displaystyle algebraic variety coordinate ring set field points varieties ideal sets defined point regular closed space polynomial mathrm radical

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Affine varietyis aaffine algebraic set which is not the union of two smaller algebraic sets0.90text
Affine varietyis alocally ringed space.Given an affine variety X with coordinate ring A0.90text
projective varieties are obtained by gluing affine varietiesinstance ofgeneral algebraic varieties0.80text
Affine varietyrelated to Affine algebraic groupsAn0.60section
Affine varietyrelated to ExamplesThe0.60section
Affine varietyrelated to ExamplesIts0.60section
Affine varietyrelated to ExamplesFor0.60section
Affine varietyrelated to ExamplesIn0.60section
Affine varietyrelated to ExamplesAlgebraic0.60section
Affine varietyrelated to ExamplesExamples0.60section
Affine varietyrelated to ExamplesOn0.60section
Affine varietyrelated to ExamplesHartogs0.60section

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