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Function field of an algebraic variety

In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient…

Geometry of the function field, Definition for complex manifolds & Generalization to arbitrary scheme

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Geometry of the function field

Field extensionTranscendence degreeDimensionAlgebraic function fieldsBirational geometry
5 related topics

Definition for complex manifolds

Complex analytic varietiesComplex analysisFieldRiemann sphere
4 related topics

Generalization to arbitrary scheme

Scheme theoryIntegral domainStalkGeneric point
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Projective lineAffine algebraic plane curveTranscendental
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Definition for complex manifolds

Construction in algebraic geometry

Generalization to arbitrary scheme

Geometry of the function field

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Function field of an algebraic variety

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field function algebraic functions geometry variety affine displaystyle complex meromorphic point rational scheme defined fractions also coordinate open subset ring

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