Geodesic
Degenerate Poisson structures in dimension 3
Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 579-592

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Formal normal forms of degenerate Poisson structures in dimension 3 are described. The main tool of the study is a spectral sequence previously introduced by the author. In particular, this method allows one to obtain a new proof of the linearizability of Poisson structures with semisimple linear part. However, there are nonlinearizable Poisson structures in dimension 3 as well. 
@article{MZM_1998_63_4_a10,
     author = {O. V. Lychagina},
     title = {Degenerate {Poisson} structures in dimension 3},
     journal = {Matemati\v{c}eskie zametki},
     pages = {579--592},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a10/}
}
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O. V. Lychagina. Degenerate Poisson structures in dimension 3. Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 579-592. http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a10/