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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| Format: | Journal article |
| Language: | English |
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Duke University Press
2020
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| _version_ | 1797095940298899456 |
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| author | Browning, T |
| author_facet | Browning, T |
| author_sort | Browning, T |
| collection | OXFORD |
| description | 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
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. This confirms the modified Manin conjecture for this variety, in which the removal of a “thin” set of rational points is allowed. |
| first_indexed | 2024-03-07T04:35:09Z |
| format | Journal article |
| id | oxford-uuid:cfae27f7-2f15-47bf-83d5-3e79541fedf4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:35:09Z |
| publishDate | 2020 |
| publisher | Duke University Press |
| record_format | dspace |
| spelling | oxford-uuid:cfae27f7-2f15-47bf-83d5-3e79541fedf42022-03-27T07:44:21ZDensity of rational points on a quadric bundle in P 3 × P 3Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cfae27f7-2f15-47bf-83d5-3e79541fedf4EnglishSymplectic ElementsDuke University Press2020Browning, TWe 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. |
| spellingShingle | Browning, T Density of rational points on a quadric bundle in P 3 × P 3 |
| title | Density of rational points on a quadric bundle in P 3 × P 3 |
| title_full | Density of rational points on a quadric bundle in P 3 × P 3 |
| title_fullStr | Density of rational points on a quadric bundle in P 3 × P 3 |
| title_full_unstemmed | Density of rational points on a quadric bundle in P 3 × P 3 |
| title_short | Density of rational points on a quadric bundle in P 3 × P 3 |
| title_sort | density of rational points on a quadric bundle in p 3 p 3 |
| work_keys_str_mv | AT browningt densityofrationalpointsonaquadricbundleinp3p3 |