On classical de Sitter solutions in higher dimensions

We derive necessary criteria for the existence of classical meta-stable de Sitter solutions in flux compactifications of type II supergravity down to dimensions higher than 4. We find that the possibilities in higher dimensions are much more restricted than in four dimensions. The only models that satisfy the criteria are derived from O6 compactifications to D = 5, 6 and O5 compactifications to D = 5, and no meta-stable solutions can exist in dimensions higher than 6. All these models have in common that the compact dimensions are negatively curved. (paper)