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Flat morphism

In mathematics, in particular in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e.,

Art, Properties of flat morphisms & Examples/non-examples

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Overview

Examples/non-examples

Properties of flat morphisms

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Map overview Semantic statistics

Flat morphism

Nodes59
Edges58
Triples17
Avg. degree1.97
Density0.033898
Components1

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Flat morphism

Top relations

related to Hilbert schemes · 6
Flat morphism → Hilb, Hilbert, Phi, Since, The, This
related to Fundamental properties · 4
Flat morphism → Flatness, If, Suppose, The
related to Miracle flatness · 4
Flat morphism → Cohen, Easy, Macaulay, Other
is a · 2
Flat morphism → blowup since a flat morphism necessarily has equi-dimensional fibers, pullback from some Hilbert scheme
see also · 1
Flat morphism → Cartier

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Important terminology

flat displaystyle morphism finite faithfully morphisms colon quasi-compact flatness locally closed every y' schemes pullback respectively presentation map noetherian de

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Flat morphismis apullback from some Hilbert scheme0.90text
Flat morphismis ablowup since a flat morphism necessarily has equi-dimensional fibers0.90text
Flat morphismrelated to Fundamental propertiesThe0.60section
Flat morphismrelated to Fundamental propertiesFlatness0.60section
Flat morphismrelated to Fundamental propertiesIf0.60section
Flat morphismrelated to Fundamental propertiesSuppose0.60section
Flat morphismrelated to Hilbert schemesThe0.60section
Flat morphismrelated to Hilbert schemesHilbert0.60section
Flat morphismrelated to Hilbert schemesThis0.60section
Flat morphismrelated to Hilbert schemesSince0.60section
Flat morphismrelated to Hilbert schemesPhi0.60section
Flat morphismrelated to Hilbert schemesHilb0.60section

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