Rational approximations on toric varieties

Zhizhong Huang

Published 2018-09-06Version 1

Using 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 hypothesis the best approximations 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 minimal centred primitive collections of the fan.