We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers. Given the intrinsically coupled translational and rotational dynamics of such vehicles, we first discuss some assumptions for the considered systems to reject torque disturbances and to balance the gravity force, which are translated into a geometric characterization of the platforms that is usually fulfilled by both standard models and more general configurations. Hence, we propose a control strategy based on the identification of a zero-moment direction for the applied force and the dynamic state feedback linearization around this preferential direction, which allows to asymptotically stabilize the platform to a static hovering condition. Stability and convergence properties of the control law are rigorously proved through Lyapunov-based methods and reduction theorems for the stability of nested sets. Asymptotic zeroing of the error dynamics and convergence to the static hovering condition are then confirmed by simulation results on a star-shaped hexarotor model with tilted propellers.