Possion Cohomology Rings And Isolated Singularities

In this master thesis,based on the work of A.Pichereau,we study the Poisson cohomology of two classes of Poisson algebras related to isolated singularities.In the first part,we determine the Gerstenhaber algebra structure over the Poisson cohomology of the three dimensional polynomial algebra endowed with a Poisson structure with isolated singularities.In the second part,we calculate the Gerstenhaber algebra structure over the Poisson cohomology of singular surfaces with isolated singularities.