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Smooth scheme

In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making precise the notion of a scheme with no singular points. A special case is the notion of a smooth variety over a field. Smooth schemes play the role in algebraic geometry of manifolds in topology.

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Overview

Definition

Properties

Generic smoothness

Examples

Advanced semantic analysis

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Map overview Semantic statistics

Smooth scheme

Nodes43
Edges42
Triples15
Avg. degree1.95
Density0.046512
Components1

How this topic connects Entity context

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Smooth scheme

Top relations

related to Examples · 12
Smooth scheme → A1, A2, Affine, An, Fermat, For, Fp, Pn, Schubert, Spec, The, Thus
related to Properties · 3
Smooth scheme → Define, In, Then

Important terminology Word statistics

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Important terminology

smooth scheme field variety dimension affine space point smoothness finite type algebraic singular regular closed schemes geometry notion gi particular

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Smooth schemerelated to ExamplesAffine0.60section
Smooth schemerelated to ExamplesAn0.60section
Smooth schemerelated to ExamplesPn0.60section
Smooth schemerelated to ExamplesFermat0.60section
Smooth schemerelated to ExamplesA10.60section
Smooth schemerelated to ExamplesA20.60section
Smooth schemerelated to ExamplesSpec0.60section
Smooth schemerelated to ExamplesThe0.60section
Smooth schemerelated to ExamplesThus0.60section
Smooth schemerelated to ExamplesFor0.60section
Smooth schemerelated to ExamplesFp0.60section
Smooth schemerelated to ExamplesSchubert0.60section

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    Min side: 3
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