Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

Guido Carlet (1) , Hessel Posthuma (2) , Sergey Shadrin (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Korteweg-de Vries Institute for Mathematics

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.

Domaines: Géométrie différentielle [math.DG]

Guido Carlet, Hessel Posthuma, Sergey Shadrin. Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed. Journal of Differential Geometry, 2018, 108 (1), pp.63-89. ⟨10.4310/jdg/1513998030⟩. ⟨hal-01719544⟩