  Mott metal-insulator transitions in an M-fold orbitally degenerate Hubbard
model are studied by means of a generalization of the linearized dynamical
mean-field theory. The method allows for an efficient and reliable
determination of the critical interaction U_c for any integer filling n and
different M at zero temperature. For half-filling a linear dependence of U_c on
M is found. Inclusion of the (full) Hund's rule exchange J results in a strong
reduction of U_c. The transition turns out to change qualitatively from
continuous for J=0 to discontinuous for any finite J.
