  We use the Polyakov-loop extended two-flavor quark-meson model as a
low-energy effective model for QCD to study 1) the possibility of inhomogeneous
chiral condensates and its competition with a homogeneous pion condensate in
the $\mu$--$\mu_I$ plane at $T=0$ and 2) the phase diagram in the $\mu_I$--$T$
plane. In the $\mu$--$\mu_I$ plane, we find that an inhomogeneous chiral
condensate only exists for pion masses lower that 37.1 MeV and does not coexist
with a homogeneous pion condensate. In the $\mu_I$--$T$ plane, we find that the
phase transition to a Bose-condensed phase is of second order for all values of
$\mu_I$ and we find that there is no pion condensation for temperatures larger
than approximately 187 MeV. The chiral critical line joins the critical line
for pion condensation at a point, whose position depends on the Polyakov-loop
potential and the sigma mass. For larger values of $\mu_I$ these curves are on
top of each other. The deconfinement line enters smoothly the phase with the
broken $O(2)$ symmetry. We compare our results with recent lattice simulations
and find overall good agreement
