New de Sitter Solutions in Ten Dimensions and Orientifold Singularities

In previous work, we found ten-dimensional solutions to the supergravity equations of motion with a dS$_4$ factor and O8-planes. We generalize this analysis and obtain other solutions in the same spirit, with an O8$_+$ and an O6$_-$. We examine our original solutions in more detail, focusing in particular on the O8$_-$ singularities and on the issues created by their boundary conditions. We also point out some previously known supersymmetric AdS solutions with the same local behavior at their O8$_-$ singularity.