Continuing the work of Monnier [Israel J. Math. 129, 189–207 (2002)], we determine the Gerstenhaber algebra structure over the Poisson cohomology groups for a large class of Poisson structures with isolated singularities over the plane. It reveals that there exists a GAGA-type phenomenon. We give an explicit description via generators and relations for the case of simple singularities.

中文翻译：

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重新审视具有孤立奇点的平面泊松结构的泊松上同调

继续 Monnier 的工作 [Israel J. Math. 129, 189–207 (2002)]，我们确定了在平面上具有孤立奇点的一大类泊松结构的泊松上同调群上的 Gerstenhaber 代数结构。说明存在GAGA型现象。对于简单奇点的情况，我们通过生成器和关系给出了明确的描述。