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Dimension of a scheme

In algebraic geometry, the dimension of a scheme is a generalization of the dimension of an algebraic variety. Scheme theory emphasizes the relative point of view and, accordingly, the relative dimension of a morphism of schemes is also important.

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Definition

Examples

Equidimensional scheme

Relative dimension

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Dimension of a scheme

Nodes36
Edges35
Triples5
Avg. degree1.94
Density0.055556
Components1

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Dimension of a scheme

Top relations

related to Definition · 4
Dimension of a scheme → By, In, Krull, Spec
is a · 1
Dimension of a scheme → generalization of the dimension of an algebraic variety

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Important terminology

displaystyle dimension scheme operatorname irreducible equidimensional closed spec relative schemes field also ideal point affine subset open maximal -1 mathfrak

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SubjectPredicateObjectConfidenceSrc
Dimension of a schemeis ageneralization of the dimension of an algebraic variety0.90text
Dimension of a schemerelated to DefinitionBy0.60section
Dimension of a schemerelated to DefinitionIn0.60section
Dimension of a schemerelated to DefinitionSpec0.60section
Dimension of a schemerelated to DefinitionKrull0.60section

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