  In this work, we consider polar perturbations and we calculate the frequency
and damping time of the quadrupolar fundamental f -mode of compact objects,
constructed using a wide range of model-independent hybrid equations of state
that include quark matter. We give special attention to the impact of the
hadron-quark conversion speed that, in the slow case, gives rise to a branch of
slow stable hybrid stars. Moreover, we study the validity of universal
relationships proposed in the literature and find out that none of them remains
valid when slow stable hybrid stars are taken into account. This fact could
constrain the applicability of asteroseismology methods with fundamental modes
designed to estimate the properties of pulsating compact objects. We hope that
this result could be tested with the start up of the third-generation
gravitational wave observatories, which might shed some light on the f -mode
emission from compact objects.
