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Height growth under a morphism of the projective line
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Algebraic geometry
Normalization of an algebraic curve
Geometric genus
Genus one curve
Elliptic curve
Naive height on the projective line
2026-10-03
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If
F
:
P
1
→
P
1
is
a
morphism
of degree
d
over
Q
, there are positive
constants
c
1
,
c
2
such that
c
1
H
(
P
)
d
≤
H
(
F
(
P
))
≤
c
2
H
(
P
)
d
(1)
for every
P
∈
P
1
(
Q
)
.
Ancestors
(10)
Naive height on the projective line
Elliptic curve
Genus one curve
Geometric genus
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
/
2019
/
iii
/
Paper 125
/
5
/
a
/
Solution
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