We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer–Manin obstruction interpolating between Manin’s classical version for rational points and the integral version developed by Colliot-Thélène and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer–Manin obstruction to account for its integral counterpart for affine quadrics.

我们研究半积分点的两个概念的局部-全局原理，称为 Campana 点和 Darmon 点。特别是，我们开发了 Brauer-Manin 障碍的半积分版本，在 Manin 的有理点经典版本和 Colliot-Thélène 和 Xu 开发的积分版本之间进行插值。我们确定了局部-全局原则的状态，以及它们所面临的障碍，在自然与二次超曲面相关的两类球形折叠中。此外，我们建立了一个定量结果，测量半积分 Brauer-Manin 障碍无法解释其仿射二次曲面的积分对应物。