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Dimension from the function field
...
Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
Algebraic variety
Function field of an algebraic variety
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Words: 21
For an irreducible variety
X
over a field
k
,
dim
X
=
trdeg
k
k
(
X
)
.
(28)
Consequently birational irreducible varieties have the same dimension.
Ancestors
(7)
Function field of an algebraic variety
Algebraic variety
Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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