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Normalization of y squared equals x times x minus one squared
(
y
2
=
x
(
x
−
1
)
2
)
...
Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
Normalization of an algebraic curve
Normalization of a nodal curve
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Words: 35
For the nodal affine cubic
y
2
=
x
(
x
−
1
)
2
, the rational parameter
t
=
x
−
1
y
(46)
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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