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Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric…

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Overview

Overview and definitions

Examples

Basic results

Isomorphism of algebraic varieties

Discussion and generalizations

Algebraic manifolds

Sources

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Map overview Semantic statistics

Algebraic variety

Nodes155
Edges154
Triples66
Avg. degree1.99
Density0.012903
Components1

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Algebraic variety

Top relations

related to Abstract varieties · 18
Algebraic variety → Alexander Grothendieck's, Algebraic Geometry, André Weil, Chapter, Classical, Claude Chevalley, For, Foundations, Furthermore, Hartshorne, However, In, In Grothendieck's, P1, Segre, So, The, Veronese
related to Non-affine and non-projective example · 10
Algebraic variety → A1, A2, An, Another, Examples, Here, It, Morphism, P1, To
related to Non-examples · 10
Algebraic variety → A1, Consider, For, GLn, Note, On, Over, SLn, The, This
related to Discussion and generalizations · 8
Algebraic variety → An, Basically, It, Strictly, Such, The, This, To
related to Algebraic manifolds · 7
Algebraic variety → Algebraic, An, Equivalently, Nash, Projective, The Riemann, When
related to Basic results · 4
Algebraic variety → An, Every, See Dimension, The
see also · 3
Algebraic variety → Analytic, Riemann, Variety
is a · 1
Algebraic variety → particular kind of scheme

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Important terminology

variety algebraic varieties affine set projective example closed space called one curve polynomial field definition group line also subset ring

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic varietyis aparticular kind of scheme0.90text
Chern classes.Jacobian varietyinstance ofwhich is important in the study of characteristic classes0.80text
abelian varietyLet C be a smooth complete curveinstance ofwhich is important in the study of characteristic classes0.80text
Picinstance ofwhich is important in the study of characteristic classes0.80text
the moduli of curves of fixed genus is typically not a projective varietyinstance ofModuli0.80text
Chern classesinstance ofwhich is important in the study of characteristic classes0.80text
Algebraic varietyrelated to Abstract varietiesIn0.60section
Algebraic varietyrelated to Abstract varietiesFor0.60section
Algebraic varietyrelated to Abstract varietiesChapter0.60section
Algebraic varietyrelated to Abstract varietiesHartshorne0.60section
Algebraic varietyrelated to Abstract varietiesSo0.60section
Algebraic varietyrelated to Abstract varietiesThe0.60section

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