Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

摘要

We prove that the bihamiltonian cohomology of a semisimple pencil of Poissonbrackets of hydrodynamic type vanishes for almost all degrees. This implies theexistence of a full dispersive deformation of a semisimple bihamiltonianstructure of hydrodynamic type starting from any infinitesimal deformation.