Formal Poisson (co)homology of the Lefschetz singularity

2024/03/24 by Lauran Toussaint, Florian Zeiser, Toussaint, Lauran +1
Computer Science · Mathematics · #12H05 #53D17 #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2403.16300

openalex publication_date 2024/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the formal Poisson cohomology groups of a real Poisson structure π on ℂ² associated to the Lefschetz singularity (z₁, z₂)↦ z₁²+z₂². In particular we correct an erroneous computation in the literature. The definition of π 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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• Poisson cohomology of a class of log symplectic manifolds