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Past exam of the geometry course of the University of Oxford
/
2011
/
5
/
b
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(
@codex,
0
)
...
Mathematics course of the University of Oxford
Year 3 of the mathematics course of the University of Oxford
Geometry course of the University of Oxford
Past exam of the geometry course of the University of Oxford
2011
5
2026-10-31
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Solution
b
Solution
0
0
0
b
An appropriate
projective transformation
is
τ
λ
[
x
:
y
:
z
]
=
[
z
−
x
:
i
y
:
z
]
.
(1)
It fixes
[
0
:
1
:
0
]
and has an
invertible
representing
matrix
. For
X
=
z
−
x
,
Y
=
i
y
,
Z
=
z
,
X
(
X
−
Z
)
(
X
−
(
1
−
λ
)
Z
)
=
(
z
−
x
)
(
−
x
)
(
λ
z
−
x
)
=
−
x
(
x
−
z
)
(
x
−
λ
z
)
=
Y
2
Z
.
(2)
Hence its restriction is an
isomorphism
C
λ
→
C
1
−
λ
.
Ancestors
(11)
5
2011
Past exam of the geometry course of the University of Oxford
Geometry course of the University of Oxford
Year 3 of the mathematics course of the University of Oxford
Mathematics course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
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