Multi-charged geometries with cosmological constant

Motivated by gauged supergravities, we consider gravitational systems coupled to arbitrary numbers of fluxes and scalar fields. We show that simple ansatze for asymptotically AdS solutions in these systems fully determine the potential for the scalars, and we construct the black hole geometries which generalize the solutions known in gauged supergravities to an arbitrary number of dimensions. We also construct branes and brane intersections supported by an arbitrary number of higher-form fluxes and a correlated number of scalars.