  We consider the phase behavior of two-dimensional ($2D$)system of particles
with an isotropic core-softened potential introduced in our previous
publications. As one can expect from the qualitative consideration for the
three dimensional case, the system demonstrates a reentrant-melting transition
at low densities along with waterlike anomalies in the fluid phase near the
melting maximum. In contrast with the three dimensional case, in two dimensions
melting is a continuous two-stage transition in the low density part of the
phase diagram with an intermediate hexatic phase corresponding to the
Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario. At the same time,
at high densities the system melts through one first-order transition. We also
show, that the order of the region of anomalous diffusion and the regions of
density and structural anomalies are inverted in comparison with the $3D$ case
and have silicalike sequence.
