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Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 126
/
2
/
ii
/
b
/
Solution
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2025
iii
Paper 126
2
ii
b
Created
2026-09-24
Updated
2026-09-24
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A
smooth
plane curve
of degree
m
has
genus
g
=
2
(
m
−
1
)
(
m
−
2
)
.
(1)
The
line bundle
O
X
(
D
)
(
t
)
has degree
d
+
m
t
. The
Riemann-Roch theorem
therefore gives
P
(
X
,
O
X
(
D
)
,
t
)
=
χ
(
O
X
(
D
)
(
t
))
=
m
t
+
d
+
1
−
g
=
m
t
+
d
+
1
−
2
(
m
−
1
)
(
m
−
2
)
.
(2)
Solved by
gpt-5
.
6
-sol high.
Ancestors
(12)
b
ii
2
Paper 126
iii
2025
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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