Density of rational points on a quadric bundle in $\mathbb{P}^3\times \mathbb{P}^3$
| Autor: | Browning, T. D., Heath-Brown, D. R. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Duke Math. J. 169, no. 16 (2020), 3099-3165 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/00127094-2020-0031 |
| Popis: | An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface $x_1y_1^2+\dots+x_4y_4^2=0$ in $\mathbb{P}^3\times\mathbb{P}^3$. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed. Comment: 60 pages; minor edits and added a reference to recent work of Lehmann and Tanimoto, where it is confirmed that the thin set we remove is the one predicted by the Lehmann-Sengupta-Tanimoto machinery |
| Databáze: | arXiv |
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