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Generic hyperplane section of a projective curve
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
Degree of a projective curve
Created
2026-09-24
Updated
2026-09-24
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For
a
general
linear form
ℓ
not vanishing identically on
a
projective curve
, the
exact sequence
0
→
A
C
(
−
1
)
ℓ
A
C
→
A
C
/
(
ℓ
)
→
0
(1)
shows that the
hyperplane-section
length
is
P
C
(
m
)
−
P
C
(
m
−
1
)
=
de
g
C
.
Ancestors
(6)
Degree of a projective curve
Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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