  For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we
give a simple characterization for when it has only log canonical, log terminal
or rational singularities. Moreover we are able to give formulas for the
plurigenera of isolated singular points of such varieties and of the
logarithmic Kodaira dimension of $V\backslash \{0\}$. For this purpose we
introduce sheaves of $m$-canonical and $L^{2,m}$-canonical forms on normal
complex spaces. For the case of affine varieties with good ${\bf C}^*$-action
we give an explicit formula for these sheaves in terms of the grading of the
dualizing sheaf and its tensor powers.
