Lemma 13.1.
Assuming that:
f
1
,
f
2
∈
ℚ
[
X
1
,
X
2
]
coprime homogeneous polynomials of degree
d
let
F
:
ℙ
1
→
ℙ
1
(
x
1
:
x
2
)
↦
(
f
1
(
x
1
,
x
2
)
:
f
2
(
x
1
,
x
2
)
)
Then
there exist
c
1
,
c
2
>
0
such that for all
P
∈
ℙ
1
(
ℚ
)
,
c
1
H
(
P
)
d
≤
H
(
F
(
P
)
)
≤
c
2
H
(
P
)
d
.