  The hyperspherical adiabatic expansion is combined with complex scaling and
used to calculate low-lying nuclear resonances of $^{12}$C in the
$3\alpha$-model. We use Ali-Bodmer potentials and compare results for other
potentials $\alpha-\alpha$ with similar $^{8}$Be-properties. A three-body
potential is used to adjust the $^{12}$C-resonance positions to desired values
extending the applicability of the method to many-body systems decaying into
three $\alpha$-particles. For natural choices of three-body potentials we find
14 resonances below the proton separation threshold, i.e. two $0^{+}$, three
$2^{+}$, two $4^{+}$, one of each of $1^{\pm}$, $2^{-}$, $3^{\pm}$, $4^{-}$,
and $6^{+}$. The partial wave decomposition of each resonance is calculated as
function of hyperradius. Strong variation is found from small to large
distance. Connection to previous experimental and theoretical results are
discussed and agreements as well as disagreements are emphasized.
