  In this paper, we study formal deformations of Poisson structures, especially
for three families of Poisson varieties in dimensions two and three. For these
families of Poisson structures, using an explicit basis of the second Poisson
cohomology space, we solve the deformation equations at each step and obtain a
large family of formal deformations for each Poisson structure which we
consider. With the help of an explicit formula, we show that this family
contains, modulo equivalence, all possible formal deformations. We show
moreover that, when the Poisson structure is generic, all members of the family
are non-equivalent.
