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We study local-global principles for two notions of semi-integral points,termed Campana points and Darmon points. In particular, we develop asemi-integral version of the Brauer-Manin obstruction interpolating betweenManin's classical version for rational points and the integral versiondeveloped by Colliot-Th\'el\`ene and Xu. We determine the status oflocal-global principles, and obstructions to them, in two families of orbifoldsnaturally associated to quadric hypersurfaces. Further, we establish aquantitative result measuring the failure of the semi-integral Brauer-Maninobstruction to account for its integral counterpart for affine quadrics.

Semi-integral Brauer-Manin obstruction and quadric orbifold pairs