References & Citations
Mathematics > Symplectic Geometry
Title: Formal Poisson (co)homology of the Lefschetz singularity
(Submitted on 24 Mar 2024)
Abstract: We compute the formal Poisson cohomology groups of a real Poisson structure $\pi$ on $\mathbb{C}^2$ associated to the Lefschetz singularity $(z_1, z_2)\mapsto z_1^2+z_2^2$. In particular we correct an erroneous computation in the literature. The definition of $\pi$ depends on a choice of volume form. Using the main result we formally classify all Poisson structure arising from different choices of volume forms.
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