We say that a subset of [Formula: see text] is maximally singular if its contains points with [Formula: see text]-linearly independent homogenous coordinates whose uniform exponent of simultaneous rational approximation is equal to [Formula: see text], the maximal possible value. In this paper, we give a criterion which provides many such sets including Grassmannians. We also recover a result of the author and Roy about a class of quadratic hypersurfaces.

中文翻译：

---

一类有理逼近的极大奇异集

我们说 [Formula: see text] 的子集是最大奇异的，如果它包含具有 [Formula: see text] - 线性独立齐次坐标的点，其同时有理逼近的一致指数等于 [Formula: see text]，最大值可能的价值。在本文中，我们给出了一个标准，它提供了许多这样的集合，包括 Grassmannians。我们还恢复了作者和 Roy 关于一类二次超曲面的结果。