Desingularizing b^m-symplectic structures
Document typeExternal research report
Rights accessOpen Access
A 2n-dimensional Poisson manifold (M,¿) is said to be bm-symplectic if it is symplectic on the complement of a hypersurface Z and has a simple Darboux canonical form at points of Z which we will describe below. In this paper we will discuss a desingularization procedure which, for m even, converts ¿ into a family of symplectic forms ¿¿ having the property that ¿¿ is equal to the bm-symplectic form dual to ¿ outside an ¿-neighborhood of Z and, in addition, converges to this form as ¿ tends to zero in a sense that will be made precise in the theorem below. We will then use this construction to show that a number of somewhat mysterious properties of bm-manifolds can be more clearly understood by viewing them as limits of analogous properties of the ¿¿'s. We will also prove versions of these results for m odd; however, in the odd case the family ¿¿ has to be replaced by a family of folded symplectic forms.
CitationMiranda, E. "Desingularizing b^m-symplectic structures". 2015.
URL other repositoryhttp://arxiv.org/abs/1512.05303