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

Renan Lima

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

Symplectic Geometry 2023-01-31 v2

Authors: Renan Lima

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.

Keywords

poisson geometry

Cite

@article{arxiv.1610.03889,
  title  = {An Example of Rank 2 Poisson Structure which is Stable Under Deformations},
  author = {Renan Lima},
  journal= {arXiv preprint arXiv:1610.03889},
  year   = {2023}
}

Comments

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

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

Abstract

Keywords

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