Poisson cohomology in dimension two

It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures onG ² (G=ℝ or ℂ) and recall a result given by Arnold. Then we will compute locally the Poisson cohomology of a particular type of Poisson structure.