Poisson cohomology in dimension three. (Q1764115)

The author considers the affine space F3 and describes the Poisson cohomology for Poisson structures on F3 in the case when there is a quasi-homogeneous Casimir. The Poisson cohomology, introduced by Lichnerowicz, plays an important role in the study of Poisson deformations. However, its computation in the general case is very difficult. In this paper, the author describes this cohomology for the affine space F3 which admits a quasi-homogeneous Casimir \(\phi\) and a singular locus reduced to the origin. She proves that this cohomology is strongly related to the singularity of the surface defined by the zero of \(\phi\).