For the degenerate bivector π = y^n ∂_x ∧ ∂_y with n>1, the classical and logarithmic Poisson cohomology groups are isomorphic in every degree.
Laurent-Gengoux, A
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On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane
For the degenerate bivector π = y^n ∂_x ∧ ∂_y with n>1, the classical and logarithmic Poisson cohomology groups are isomorphic in every degree.