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arXiv · 1809.02001

Rational approximations on toric varieties

Zhizhong Huang
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Abstract

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.

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Zhizhong Huang. 2018-09-06. Rational approximations on toric varieties. https://doi.org/10.2140/ant.2021.15.461

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