The geometric exceptional set in Manin's conjecture for Batyrev and Tschinkel's example
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917850571079680 |
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| author | Gao, Runxuan |
| author_facet | Gao, Runxuan |
| contents | Batyrev and Tschinkel's example is a Fermat cubic surface bundle $X$ which is a Fano $5$-fold. It is the first example for which Manin's conjecture can never hold for a proper closed exceptional set. Recently, Lehmann, Sengupta, and Tanimoto proposed a conjectural geometric description of the exceptional set in Manin's conjecture and showed that it is always contained in a thin set. Over a field of characteristic $0$, we explicitly construct finitely many thin maps such that any thin map $f:Y\rightarrow X$ with equal or larger $a$- and $b$-values in lexicographical order factors rationally through one of them. In particular, this defines a thin set which coincides with Lehmann-Sengupta-Tanimoto's conjectural exceptional set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04138 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometric exceptional set in Manin's conjecture for Batyrev and Tschinkel's example Gao, Runxuan Algebraic Geometry Number Theory Batyrev and Tschinkel's example is a Fermat cubic surface bundle $X$ which is a Fano $5$-fold. It is the first example for which Manin's conjecture can never hold for a proper closed exceptional set. Recently, Lehmann, Sengupta, and Tanimoto proposed a conjectural geometric description of the exceptional set in Manin's conjecture and showed that it is always contained in a thin set. Over a field of characteristic $0$, we explicitly construct finitely many thin maps such that any thin map $f:Y\rightarrow X$ with equal or larger $a$- and $b$-values in lexicographical order factors rationally through one of them. In particular, this defines a thin set which coincides with Lehmann-Sengupta-Tanimoto's conjectural exceptional set. |
| title | The geometric exceptional set in Manin's conjecture for Batyrev and Tschinkel's example |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2311.04138 |