On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918477089996800 |
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| author | Kari, Kamtila Bruno, Iskamlé Éméry, Diekouam Fotso Luc Calvin, Tcheka |
| author_facet | Kari, Kamtila Bruno, Iskamlé Éméry, Diekouam Fotso Luc Calvin, Tcheka |
| contents | In this paper, we show that for a given degenerate bivector $π= y^n\partial_x \wedge \partial_y$ 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 dégrée. 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 $π$. $\mathbb{F}$ is the field of characteristic 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00217 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane Kari, Kamtila Bruno, Iskamlé Éméry, Diekouam Fotso Luc Calvin, Tcheka Algebraic Geometry In this paper, we show that for a given degenerate bivector $π= y^n\partial_x \wedge \partial_y$ 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 dégrée. 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 $π$. $\mathbb{F}$ is the field of characteristic 0. |
| title | On logarithmic Poisson cohomology of a degenerate Poisson bivector in affine plane |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.00217 |