  We prove a new patchworking theorem for singular algebraic curves, which
states the following. Given a complex toric threefold $Y$ which fibers over
${\mathbb C}$ with a reduced reducible zero fiber $Y_0$ and other fibers $Y_t$
smooth, and given a reduced curve $C_0\subset Y_0$, the theorem provides a
sufficient condition for the existence of a one-parametric family of curves
$C_t\subset Y_t$, which induces an equisingular deformation for some singular
points of $C_0$ and certain prescribed deformations for the other
singularities. As application we give a comment on a recent theorem by G.
Mikhalkin on enumeration of nodal curves on toric surfaces via non-Archimedean
amoebas [arXiv:math.AG/0209253]. Namely, using our patchworking theorem, we
establish link between nodal curves over the field of complex Puiseux series
and their non-Archimedean amoebas, what has been done by Mikhalkin in a
different way. We discuss also the case of curves with a cusp as well as real
nodal curves.

Algebraic Geometry