arXiv 1805.044352018-05math.DGmath-phmath.MPmath.QAmath.SG

Poisson Cohomology of Broken Lefschetz Fibrations

Panagiotis Batakidis, Ramón Vera

备注：: Final version, 30pp
发表信息：: Differential Geometry and its Applications 72 (2020) 101661

英文摘要：

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.

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