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arXiv · 1501.04295

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

Guido Carlet·Hessel Posthuma·Sergey Shadrin
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Abstract

We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.

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Guido Carlet, Hessel Posthuma, Sergey Shadrin. 2015-01-18. Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed. https://doi.org/10.4310/jdg%2F1513998030

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