  We advance support variety theory for finite tensor categories. First we show
that the dimension of the support variety of an object equals the rate of
growth of a minimal projective resolution as measured by the Frobenius-Perron
dimension. Then we show that every conical subvariety of the support variety of
the unit object may be realized as the support variety of an object. Finally,
we show that the support variety of an indecomposable object is connected.
