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Picard lattice of a Hirzebruch surface
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Mathematics
Area of mathematics
Geometry and topology
Algebraic geometry
Algebraic surface
Intersection pairing on the Picard group of a surface
2026-09-28
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For the
Hirzebruch surface
F
n
, the
negative section of a Hirzebruch surface
S
and
a
fiber class of a Hirzebruch surface
F
freely generate
Pic
(
F
n
)
and satisfy
S
2
=
−
n
,
S
⋅
F
=
1
,
F
2
=
0.
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Intersection pairing on the Picard group of a surface
Algebraic surface
Algebraic geometry
Geometry and topology
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 159
/
1
/
Solution
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