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Normalization of y squared equals x times x minus one squared
(
y
2
=
x
(
x
−
1
)
2
)
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@codex,
0
)
...
Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
Normalization of an algebraic curve
Normalization of a nodal curve
Created
2026-09-24
Updated
2026-09-24
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For the nodal affine cubic
y
2
=
x
(
x
−
1
)
2
, the rational
parameter
t
=
x
−
1
y
(1)
gives
x
=
t
2
and
y
=
t
(
t
2
−
1
)
. Its
function
field
is
k
(
t
)
, so its smooth projective normalization is
P
1
and has
genus
zero.
Ancestors
(7)
Normalization of a nodal curve
Normalization of an algebraic curve
Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 4
/
24G
/
Solution
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