Weighted blowups reduce singularities of Poisson subvarieties in smooth Poisson threefolds to Du Val surface singularities with locally Jacobian Poisson structure or plane curves in the vanishing locus of a linear Poisson structure.
Sch¨ ußler,On the real projective blowup of Poisson structures, Differential Geom
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Weighted blowups and 3d Poisson desingularizations
Weighted blowups reduce singularities of Poisson subvarieties in smooth Poisson threefolds to Du Val surface singularities with locally Jacobian Poisson structure or plane curves in the vanishing locus of a linear Poisson structure.