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Density of rational points on a quadric bundle in P 3 × P 3

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Files:
Publisher copy:
10.1215/00127094-2020-0031
Publisher:
Duke University Press
Journal:
Duke Mathematical Journal More from this journal
Volume:
169
Issue:
16
Pages:
3099-3165
Publication date:
2020-11-01
Acceptance date:
2020-03-24
DOI:
EISSN:
1547-7398
ISSN:
0012-7094
Language:
English
Keywords:
Pubs id:
1096447
Local pid:
pubs:1096447
Deposit date:
2020-03-25

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