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arXiv · 2605.00217

On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane

Kamtila Kari·Iskamlé Bruno·Diekouam Fotso Luc Éméry·Tcheka Calvin
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Abstract

In this paper, we show that for a given degenerate bivector $\pi= y^n\partial_x \wedge \partial_y$ with $n>1$, the classical Poisson cohomology group and the logarithmic Poisson cohomology group along the ideal $\mathcal{I}=y^n\mathbb{F}[x,y] $ are isomorphics in every d\'egr\'ee. This result follows from determination of the logarithmic Hamiltonian operator and the logarithmic Poisson cochain complexe in order to compute the cohomological invariants associated to $\pi$. $\mathbb{F}$ is the field of characteristic 0.

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Kamtila Kari, Iskamlé Bruno, Diekouam Fotso Luc Éméry, Tcheka Calvin. 2026-04-30. On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane. https://arxiv.org/abs/2605.00217

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