Rational approximations on toric varieties
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866908477191880704 |
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| author | Huang, Zhizhong |
| author_facet | Huang, Zhizhong |
| contents | Using the universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain geometric hypothesis the best approximations (in the sense of McKinnon-Roth's work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves correspond, according to Batyrev's terminology, to the centred primitive collections of the fan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_02001 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Rational approximations on toric varieties Huang, Zhizhong Number Theory Algebraic Geometry 14G05, 14M25 Using the universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain geometric hypothesis the best approximations (in the sense of McKinnon-Roth's work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves correspond, according to Batyrev's terminology, to the centred primitive collections of the fan. |
| title | Rational approximations on toric varieties |
| topic | Number Theory Algebraic Geometry 14G05, 14M25 |
| url | https://arxiv.org/abs/1809.02001 |