An Example of Rank 2 Poisson Structure which is Stable Under Deformations

Abstract

Let $\Pi$ be a rank $2$ Poisson Structure in the Projective Space defined by the dimension $2$ foliation $\mathcal{F}$ in the pull-back component. We prove that for a generic choice of $\mathcal{F}$, the irreducible component of the Poisson structures containing $\Pi$ and the irreducible component of Foliations containing $\mathcal{F}$ coincides.

There is a serious gap about the tangent space of the dimension 2 foliations induced by a linear pull-back. I do not know if the scheme is reduced and so it is possible that the dimension of the tangent space of this scheme is bigger than his topological dimension

References in corpus (2)

• Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson brackets
• A characterization of diagonal Poisson structures