Density of rational points on a quadric bundle in P 3 × P 3
We establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski-dense subset of the biprojective hypersurface x 1 y 2 1 + ⋯ + x 4 y 2 4 = 0 in P 3 × P 3 . This confirms the modified Manin conjecture for this variety, in which the r...
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| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
Duke University Press
2020
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| Resumo: | We establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski-dense subset of the biprojective hypersurface
x
1
y
2
1
+
⋯
+
x
4
y
2
4
=
0
in
P
3
×
P
3
. This confirms the modified Manin conjecture for this variety, in which the removal of a “thin” set of rational points is allowed. |
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