  We study Poisson structures over singular varieties. In this purpose, we
consider the Koszul complex associated to the equations of a complete
intersection. This complex forms a differential graded algebra which is
equivalent to the algebra of the variety. We show that a Poisson structure is
equivalent to a sequence of multiderivations over the Koszul complex. If our
variety has isolated singularities, then we can construct a sequence of
multiderivations of reduced form.
