Dimension preserving resolutions of singularities of Poisson structures

Hichem Lassoued (1, 2)

1 UBMA - Université Badji Mokhtar [Annaba]
2 IECL - Institut Élie Cartan de Lorraine

We give examples of Poisson structures that admit symplectic resolutions of the same dimension. We also give a simple condition under which proper in the smooth case or semi-connected symplectic resolutions in the real analytic and holomorphic case can not exist : open symplectic leaves have to be dense and the singular locus can not be of codimension one.

Domaines: Géométrie différentielle [math.DG]

Hichem Lassoued. Dimension preserving resolutions of singularities of Poisson structures. 2017. ⟨hal-01487059v2⟩