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 and Roth’s work) can be achieved on rational curves passing through the fixed point of minimal degree, confirming a conjecture of McKinnon. These curves are also minimal in the sense of deformation theory, and they correspond, according to Batyrev’s terminology, to the centred primitive collections of the structural fan.

中文翻译：

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复曲面品种的有理逼近

使用Salberger提出的通用转矩方法，我们研究了复曲面复变品种上有理点的一般不动点的逼近。我们证明，在某些几何假设下，最好的近似值（就麦金农和罗斯的工作而言）可以通过经过最小程度固定点的有理曲线来实现，从而证实了麦金农的一个猜想。从变形理论的角度来看，这些曲线也是最小的，按照巴特列夫的术语，它们对应于结构风扇的居中原始集合。