We compute the formal Poisson cohomology of a broken Lefschetz fibration by calculating it at fold and Lefschetz singularities. Near a fold singularity the computation reduces to that for a point singularity in 3 dimensions. For the Poisson cohomology around singular points we adapt techniques developed for the Sklyanin algebra. As a side result, we give compact formulas for the Poisson coboundary operator of an arbitrary Jacobian Poisson structure in 4 dimensions.

中文翻译：

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Lefschetz纤维断裂的泊松同调

我们通过计算折痕和Lefschetz奇点来计算破裂的Lefschetz纤维的正式泊松同调性。接近折叠奇点时，计算将减少为3维点奇点的计算。对于围绕奇异点的泊松同调，我们采用为Sklyanin代数开发的技术。作为附带结果，我们给出了任意4维Jacobian Poisson结构的Poisson共边界算子的紧凑公式。